Question

Prove that (cosec (90- theta)- sin (90- theta)(cosec theta-sin theta)(tan theta+ cot theta) =1

Answer 1

because the sin^2 theta + cos^2 theta =1 and sec^2 theta - tan^2 =1

Answer 2

Answer:

[(cosec(90-theta)- sin(90-theta)] [(cosec theta -sin theta) (tan theta + cot theta)]

Step-by-step explanation:

(sec theta - cos theta) (cosec theta - sin theta)

sin theta / cos theta + cos theta / sin theta

cosec (90- theta)= sec theta

sin (90-theta)= cos theta

(1 - cos theta/ cos theta)(1- sin theta/sin theta)(sin2 theta +cos 2 theta /sin theta cos theta)

(1-cos2 theta/cos theta) (1-sin2 theta/sin theta) (1/ sin theta cos theta)

(sin2/cos theta)(cos2 theta/sin theta)(1/ sin theta cos theta)=1