Question

if sec theta plus tan theta =4 then find the values of cos theta tan theta

Answer 1

i think this is right

Answer 2

Given sec theta + tan theta = 4.

 On squaring both sides, we get

(sec theta + tan theta)^2 = (4)^2

We know that (a+b)^2 = a^2+b^2 + 2ab.

sec^2 theta + tan^2 theta + 2 sectheta tantheta = 16

We know that sec^2theta = tan^2theta + 1. = > tan^2 theta = sec^2 theta - 1.

sec^2 theta + sec^2 theta - 1 + 2 sectheta tantheta = 16.

2 sec^2 theta - 1 + 2 sectheta tantheta = 16

2 sec^2 theta + 2 sectheta tantheta = 16 + 1

2 sec^2 theta + 2 sectheta tantheta = 17

2 sec theta(sec theta + tan theta) = 17.

2 sec theta(4) = 17

sec theta = 17/8.

Then tan^2 theta =  sec^2 theta - 1

                              = (17/8)^2 - 1

                              =  289/64 - 1

                              = 225/64

             tan theta = (15/8)



Now,

Sin theta = tan theta/sec theta

                = 15/8/17/8

                = 15/17.


We know that sin^2 theta + cos ^2 theta = 1 

Cos^2 theta = 1 - sin^2 theta

                     = 1 - (15/17)^2

                     = 1 - 225/289

                     = 64/289

cos theta = 8/17.


Hope this helps!