Question

Sin(90-theta)/cosec(90-theta)-cot(90-theta) = 1+sin theta

Answer 1

if u have any doubt pls ask me

Answer 2

Hence proved  $\frac{\sin (90-\theta)}{\csc(90-\theta)-\cot(90-\theta)}=1+\sin \theta$

Step-by-step explanation:

Prove : $\frac{\sin (90-\theta)}{\csc(90-\theta)-\cot(90-\theta)}=1+\sin \theta$

Proof :

Taking LHS,

$LHS=\frac{\sin (90-\theta)}{\csc(90-\theta)-\cot(90-\theta)}$

Using trigonometric properties,

$\sin(90-\theta)=\cos \theta\\\csc(90-\theta)=\sec \theta\\\cot(90-\theta)=\tan\theta$

Substitute the values,

$LHS=\frac{\cos \theta}{\sec \theta-\tan \theta}$

$LHS=\frac{\cos \theta}{\frac{1}{\cos \theta}-\frac{\sin\theta}{\cos \theta}}$

$LHS=\frac{\cos^2 \theta}{1-\sin\theta}$

Using trigonometric property, $\cos^2\theta=1-\sin^2\theta$

$LHS=\frac{1-\sin^2 \theta}{1-\sin\theta}$

$LHS=\frac{(1-\sin \theta)(1+\sin\theta)}{1-\sin\theta}$

$LHS=1+\sin\theta$

$LHS=RHS$

Hence proved.

#Learn more

EVALUATE : SIN THETA + COS THETA + SIN THETA COS (90°- THETA) COS THETA / SEC(90°-theta) + cos theta sin (90-theta)sin theta /cosec(90°-theta) - 2 sin(90°-theta) cos (90°-theta)

https://brainly.in/question/2500360