The value of tan712° is equal to A6+3+2-2 B6-3+2-2 C6-3+2+2 D6-3-2-2

The true option is B 6-3+2-2Explanation for the correct optionThe given trigonometric expression: tan712°.It is known that sin(A-B)=sin(A)cos(B)-cos(A)sin(B).Therefore, sin15°=sin45°-30°⇒sin15°=sin45°cos30°-cos45°sin30°⇒sin15°=12×32-12×12⇒sin15°=322-122⇒sin15°=3-122⇒sin15°=223-1222⇒sin15°=26-28⇒sin15°=6-24It is known that cos(A-B)=cos(A)cos(B)+sin(A)sin(B).Thus, cos15°=cos45°-30°⇒cos15°=cos45°cos30°+sin45°sin30°⇒cos15°=12×32+12×12⇒cos15°=322+122⇒cos15°=3+122⇒cos15°=223+1222⇒cos15°=26+28⇒cos15°=6+24Now, tanA=sinAcosA.⇒tanA=2sinAcosA2cos2A⇒tanA=sin2A1+cos2AThus, tan712°=sin15°1+cos15°.⇒tan712°=6-241+6+24⇒tan712°=6-24+6+2⇒tan712°=6-24-6+24+6+24-6+2⇒tan712°=46-2-6-26+216-6+22⇒tan712°=46-42-6+216-6-2-212⇒tan712°=46-42-48-43⇒tan712°=6-2-12-3⇒tan712°=6-2-12+32-32+3⇒tan712°=26-22-2+18-6-34-3⇒tan712°=6-22-2+32-3⇒tan712°=6-3+2-2Hence, option B is correct.

"The value of tan712° is equal to A6+3+2-2..." was answered by our community

saussito5cl

Answered question

2023-02-12

The value of

\tan (7 {\frac{1}{2}}^{°})

is equal to A

6 + 3 + 2 - 2

6 - 3 + 2 - 2

6 - 3 + 2 + 2

6 - 3 - 2 - 2

Answer & Explanation

veitigaq

Beginner2023-02-13Added 5 answers

The true option is B

6 - 3 + 2 - 2

Explanation for the correct option
The given trigonometric expression:

\tan (7 {\frac{1}{2}}^{°})

.
It is known that

\sin (A - B) = \sin (A) \cos (B) - \cos (A) \sin (B)

.
Therefore,

\sin (15 °) = \sin (45 ° - 30 °)

\Rightarrow \sin (15 °) = \sin (45 °) \cos (30 °) - \cos (45 °) \sin (30 °) \Rightarrow \sin (15 °) = \frac{1}{2} \times \frac{3}{2} - \frac{1}{2} \times \frac{1}{2} \Rightarrow \sin (15 °) = \frac{3}{22} - \frac{1}{22} \Rightarrow \sin (15 °) = \frac{3 - 1}{22} \Rightarrow \sin (15 °) = \frac{(22) (3 - 1)}{{(22)}^{2}} \Rightarrow \sin (15 °) = \frac{2 (6 - 2)}{8} \Rightarrow \sin (15 °) = \frac{(6 - 2)}{4}

It is known that

\cos (A - B) = \cos (A) \cos (B) + \sin (A) \sin (B)

.
Thus,

\cos (15 °) = \cos (45 ° - 30 °)

\Rightarrow \cos (15 °) = \cos (45 °) \cos (30 °) + \sin (45 °) \sin (30 °) \Rightarrow \cos (15 °) = \frac{1}{2} \times \frac{3}{2} + \frac{1}{2} \times \frac{1}{2} \Rightarrow \cos (15 °) = \frac{3}{22} + \frac{1}{22} \Rightarrow \cos (15 °) = \frac{3 + 1}{22} \Rightarrow \cos (15 °) = \frac{(22) (3 + 1)}{{(22)}^{2}} \Rightarrow \cos (15 °) = \frac{2 (6 + 2)}{8} \Rightarrow \cos (15 °) = \frac{(6 + 2)}{4}

Now,

\tan (A) = \frac{\sin (A)}{\cos (A)}

\Rightarrow \tan (A) = \frac{2 \sin (A) \cos (A)}{2 \cos^{2} (A)} \Rightarrow \tan (A) = \frac{\sin (2 A)}{1 + \cos (2 A)}

Thus,

\tan (7 {\frac{1}{2}}^{°}) = \frac{\sin (15 °)}{1 + \cos (15 °)}

\Rightarrow \tan (7 {\frac{1}{2}}^{°}) = \frac{\frac{6 - 2}{4}}{1 + \frac{6 + 2}{4}} \Rightarrow \tan (7 {\frac{1}{2}}^{°}) = \frac{6}{-} \Rightarrow \tan (7 {\frac{1}{2}}^{°}) = \frac{(6 - 2)}{(4 - (6 + 2))} \Rightarrow \tan (7 {\frac{1}{2}}^{°}) = \frac{4 (6 - 2) - (6 - 2) (6 + 2)}{16 - {(6 + 2)}^{2}} \Rightarrow \tan (7 {\frac{1}{2}}^{°}) = \frac{46 - 42 - 6 + 2}{16 - 6 - 2 - 212} \Rightarrow \tan (7 {\frac{1}{2}}^{°}) = \frac{46 - 42 - 4}{8 - 43} \Rightarrow \tan (7 {\frac{1}{2}}^{°}) = \frac{6 - 2 - 1}{2 - 3} \Rightarrow \tan (7 {\frac{1}{2}}^{°}) = \frac{(6 - 2 - 1) (2 + 3)}{(2 - 3) (2 + 3)} \Rightarrow \tan (7 {\frac{1}{2}}^{°}) = \frac{26 - 22 - 2 + 18 - 6 - 3}{4 - 3} \Rightarrow \tan (7 {\frac{1}{2}}^{°}) = 6 - 22 - 2 + 32 - 3 \Rightarrow \tan (7 {\frac{1}{2}}^{°}) = 6 - 3 + 2 - 2

Hence, option B is correct.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Precalculus

Describe all solutions of Ax=0 in parametric vector form, where A is row equivalent to the given matrix
$[\begin{matrix} 1 & 3 & 0 & - 4 \\ 2 & 6 & 0 & - 8 \end{matrix}]$
Find, correct to the nearest degree, the three angles of the triangle with the given vertices
A(1, 0, -1), B(3, -2, 0), C(1, 3, 3)
Whether f is a function from Z to R if
a) $f (n) = \pm n$ .
b) $f (n) = \sqrt{n^{2} + 1}$ .
c) $f (n) = \frac{1}{n^{2} - 4}$ .
?
How to write the expression $6^{\frac{3}{2}}$ in radical form?
How to evaluate $\sin (\frac{- 5 π}{4})$ ?
What is the derivative of $\cot^{2} x$ ?
How to verify the identity: $\frac{\cos (x) - \cos (y)}{\sin (x) + \sin (y)} + \frac{\sin (x) - \sin (y)}{\cos (x) + \cos (y)} = 0$ ?
Find $\tan (22 . 5^{\circ})$ using the half-angle formula.
How to find the exact values of $\cos 22.5 °$ using the half-angle formula?
How to express the complex number in trigonometric form: 5-5i?
The solution set of $\tan θ = 3 \cot θ$ is
How to find the angle between the vector and $x -$ axis?
Find the probability of getting 5 Mondays in the month of february in a leap year.
How to find the inflection points for the given function $f (x) = x^{3} - 3 x^{2} + 6 x$ ?
How do I find the value of sec(3pi/4)?

Didn't find what you were looking for?