Question

sin theta / 1+ cos theta + 1+ cos theta / sin theta = 2 cosec theta ​

Answer 1

Answer:

Sin theta/1+cos theta + 1 +cos theta/ sin theta = 2 cosec theta is proved.

I am taking theta as A so that it is easy for explanation.

Step-by-step explanation:

= sin A / 1 + cos A + 1+ cos A/ sin A

= sin A ×sin A+ (1+ cos A)×(1+cos A) / sin A (1+ cos A)

Taking L.C.M. of sin A and 1+ cos A

= sin²A + (1+ cos A)²/ sin A (1+ cos A)

= sin²A + (1² + cos² A + 2 ×1××cos A) / sin A (1+ cos A )

= sin² A + 1+ cos²A + 2 cos A/ sin A (1+ cos A)

= 1+1+2 cos A/ sin A (1+ cos A)

= 2+2 cos A/ sin A (1+ cos A)

= 2( 1+ cos A) / sin A (1+ cos A)

Taking 2 common

= 2 / sin A

= 2× I/ sin A

= 2 cosec A = RHS

Hence, proved.