Question

if cos square x + cos to the power 4 x prove that tan square x + tan to the power 4 x is equal to 1​

Answer 1

Answer:

$tan^2x+tan^4x=1$

Step-by-step explanation:

Formula used:

$cos^2\theta+sin^2\theta=1$

Given:

$cos^2x+cos^4x=1$...........(1)

$cos^4x=1-cos^2x$

$cos^4x=sin^2x$

$cos^2x=\frac{sin^2x}{cos^2x}$

$cos^2x=tan^2x$...........(2)

squaring on both sides we get

$cos^4x=tan^4x$...........(3)

using (2) and (3) in (1) we get

$tan^2x+tan^4x=1$