Question

Evaluate Sin 15 - Cosec 26
Sec 64
Cos 75​

Answer 1

$Given \: \red{ sin 15 - Cosec 26 sec 64 cos 75 }$

$= sin 15 - Cosec 26 sec (90 - 26) cos (90 - 15)$

$= sin 15 - Cosec 26 Cosec 26 sin 15$

$= sin 15( 1 - cosec^{2} 26 )$

$= - sin 15 ( cosec^{2} 26 - 1 )$

$= - sin 15 cot^{2} 26$

/* By Trigonometric Identity */

$\boxed{ \pink { Cosec^{2} \theta - 1 = cot^{2} \theta }}$

Therefore.,

$\red{ sin 15 - Cosec 26 sec 64 cos 75 }$

$\green{ = - sin 15 cot^{2} 26 }$

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