Prove that: csc &#x2061;<!-- ⁡ --> 50 <mrow class="MJX-TeXAtom-ORD"> &#xB0; </m

woowheedr

woowheedr

Answered question

2022-07-15

Prove that: csc 50 ° + cot 100 ° = cot 25 ° csc 100 °

Answer & Explanation

Nicolas Calhoun

Nicolas Calhoun

Beginner2022-07-16Added 15 answers

csc 50 ° + cot 100 ° = cot 25 ° csc 100 °
csc 50 ° + cot 100 ° + csc 100 ° = cot 25 °
1 sin 50 ° + cos 100 ° sin 100 ° + 1 sin 100 ° = cot 25 °
1 sin 50 ° + cos 100 ° + 1 sin 100 ° = cot 25 °
1 sin 50 ° + 2 cos 2 50 ° 2 sin 50 ° cos 50 ° = cot 25 °
1 sin 50 ° + cos 50 ° sin 50 ° = cot 25 °
1 + cos 50 ° sin 50 ° = cot 25 °
2 cos 2 25 ° 2 sin 25 ° cos 25 ° = cot 25 °
Done
Frank Day

Frank Day

Beginner2022-07-17Added 4 answers

Hint:
csc 2 x + cot 2 x = 1 + cos 2 x sin 2 x = 2 cos 2 x 2 cos x sin x = cot x
Set x = 50 , 100

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