Question

sec theta+tan theta=2+root3.find cos theta?

Answer 1

tan theta + sec theta = 2

=> sec theta = 2 - tan theta

=> sec theta -2 = - tan theta

adding square on both the sides

=> (sec theta -2)^2 = (-tan theta)^2

=> (sec theta)^2 -2 *(sec theta)*2+2^2 = (+tan theta)^2

=> sec^2 theta-4 sec theta+4 = tan^2 theta

=> sec^2 theta-tan^2 theta-4 sec theta +4 = 0

=> 1-4 sec theta +4 =0 (since sec^2theta - tan^2theta = 1)

=> 5 - 4 sec theta = 0

=> 5 = 4 sec theta

=> sec theta = 5/4

Intially Given sec theta + tan theta = 2

=> tan theta = 2- sec theta

=> tan theta = 2-5/4

=> tan theta = 3/4