Find the value of cos⁡105∘+sin⁡75∘ We can write the given trig expression as cos⁡(180∘−75∘)+sin⁡75∘=−cos⁡75∘+sin⁡75∘ =sin⁡75∘−cos⁡75∘

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Find the value of cos⁡105∘+sin⁡75∘  We can write the given trig expression as  cos⁡(180∘−75∘)+sin⁡75∘=−cos⁡75∘+sin⁡75∘  =sin⁡75∘−cos⁡75∘

MoxboasteBots5h · Accepted Answer

sin⁡75∘ can be written as sin⁡(30+45)  sin⁡(30+45)=sin⁡30⋅cos⁡45+cos⁡30⋅cos⁡45  Similarly cos⁡105=cos⁡(60+45)⇒cos⁡60⋅cos⁡45−sin⁡60sin⁡45  Now just add both the above equation and try to use value from the trignometry chart below.

Navreaiw · Accepted Answer

Following on from where you left off,  sin⁡75∘−cos⁡75∘=−sin⁡(−75∘)−cos⁡(−75∘)  =−sin⁡75∘+cos⁡(−75∘)  Using the formula sin⁡θ+cos⁡θ=2sin⁡(θ+45∘)  (which can be proven using the addition formula for sin⁡), this becomes  −2sin⁡(−30∘)=2sin⁡30∘=22

karton · Accepted Answer

There&#039;s some transformation formula I&#039;m listing below, sin⁡(a+b)+sin⁡(a−b)=2sin⁡acos⁡b sin⁡(a+b)−sin⁡(a−b)=2cos⁡asin⁡b cos⁡(a+b)+cos⁡(a−b)=2cos⁡acos⁡b cos⁡(a−b)−cos⁡(a+b)=2sin⁡asin⁡b Now your problem reduces to sin⁡75∘−cos⁡75∘, to make use the above formula, we convert cos⁡75∘=sin⁡15∘ and we write 75 = 45+30 and 15 = 45-30. So we have sin⁡(45∘+30∘)−sin⁡(45∘−30∘)=2cos⁡45∘⋅sin⁡30∘=2⋅12⋅12=12 Alter: You need not break the given form even, as follows cos⁡105∘+sin⁡75∘=cos⁡105∘+cos⁡15∘=cos⁡(60+45)+cos⁡(60−45)

Find the value of \cos 105^{\circ}+\sin 75^{\circ} We can write the

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