Question

tan theta divided by 1 + secant theta minus tan theta divided by 1 minus secant theta is equal to 2 cosec theta

tan/1+sec - tan/1-sec = 2cosec​

Answer 1

Step-by-step explanation:

taking LCM we get tan theta (1- sec theta) - tan theta(1+ sec theta) whole by ( 1+sec theta)(1- sec theta)

= -2 tan theta sec theta / 1- sec² theta

= -2 tan theta sec theta /-( sec² theta-1)

= - 2 tan theta sec theta / - tan² theta

= 2 sec theta/ tan theta

= 2/ cos theta / sin theta / cos theta

= 2 / sin theta

= 2 CSC theta

hence proved

formulae used:

a²- b²= ( a+ b)( a-b)

sec theta = 1/ cos theta

tan theta = sin theta/ cos theta

CSC theta = 1/ sin theta

sec² theta -1= tan² theta

hope it helped you