Question

cos theta + sec theta is equal to K then what is the value of sin square theta minus tan square theta​

Answer 1

Steps:

let theta = x

cosx + secx=k

on squaring both sides

cos^2x+sec^2x+2cosxsecx=k^2

As, cosx = 1/sec

so,

cos^2x+sec^2x+2=k^2_____(1)

As we know,

1-sin^2x=cos^2x___(2)

and

1+tan^2x=sec^2x___(3)

so from equation 1,2 and 3

1-sin^2x + 1+tan^2x + 2 = k^2

=> -sin^2x + tan^2x = k^2 - 4

by multiplying minus on both sides

sin^2x - tan^2x = 4 - k^2

Answer:

4 - k^2