Is tan^4(k)-sec^4(k)=1-2sec^2(k) ?

The answer to whether tan^4(k)-sec^4(k)=1-2sec^2(k) is True

Popular >

prove tan^4(k)-sec^4(k)=1-2sec^2(k)

prove

tan^{4} (k) - sec^{4} (k) = 1 - 2 sec^{2} (k)

True

Solution steps

tan^{4} (k) - sec^{4} (k) = 1 - 2 sec^{2} (k)

Manipulating left side

tan^{4} (k) - sec^{4} (k)

Factor

- sec^{4} (k) + tan^{4} (k) : (tan^{2} (k) + sec^{2} (k)) (tan (k) + sec (k)) (tan (k) - sec (k))

= (- sec (k) + tan (k)) (sec (k) + tan (k)) (sec^{2} (k) + tan^{2} (k))

Rewrite using trig identities

= 1 - 2 sec^{2} (k)

We showed that the two sides could take the same form

\Rightarrow True

tan^{2} (x) + 5 = sec^{2} (x) + 4

1 - tan^{4} (x) = 2 sec^{2} (x) - sec^{4} (x)

sin (π) = sin (- π)

csc^{2} (x) + 2 cot (x) = (1 + cot (x))^{2}

csc (t) cot (t) = \frac{1 + cot ^{2} ( t )}{sec ( t )}

Is tan^4(k)-sec^4(k)=1-2sec^2(k) ?
The answer to whether tan^4(k)-sec^4(k)=1-2sec^2(k) is True