Question

prove that sin 34/sin 56+cos34/cos 56=sec 34.cosec 34.

Answer 1

Answer:

$\frac{sin 34}{sin 56}+ \frac{cos 34}{cos 56}= sec 34 cosec 34$

Step-by-step explanation:

$LHS = \frac{sin 34}{sin 56}+ \frac{cos 34}{cos 56}$

$= \frac{sin 34}{sin(90- 34)}+ \frac{cos 34}{cos(90-34)}$

$= </p><p>\frac{sin 34}{cos 34}+ \frac{cos 34}{sin 34}$

$= \frac{ sin^{2} 34 + cos^{2} 34}{cos 34 sin 34 }$

$= \frac{1}{ cos34 sin 34 }$

/* By Trigonometric identity :

sin²x + cos²x = 1 */

$= sec 34 cosec 34$

$= RHS$

Therefore.,

$\frac{sin 34}{sin 56}+ \frac{cos 34}{cos 56}= sec 34 cosec 34$

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