tan^4x-sec^4x=1-2 sec^2(x)
verify

Question

tan^4x-sec^4x=1-2 sec^2(x)
verify

harsimran_hs4 · Answer

use equation generator other your question can be interpreted in many ways

anonymous · Answer

$$\tan^4x-\sec^4x=1-2 \sec^2(x)$$

harsimran_hs4 · Answer

consider LHS
since we need final answer in sec x we will try and substitute tanx in terms of sec x

we know sec^2 x = 1 + tan^2 x
tan^2 x = sec^2 x - 1
tan^4 x = (sec^2 x - 1)^2
= sec^4 x + 1 - 2sec^2 x

can you proceed now??

anonymous · Answer

let me work on it and see

anonymous · Answer

LHS

$$=(\sec ^{2}x-1)^{2}-\sec ^{4}x$$
$$=\sec ^{4}x+1-\sec ^{4}x$$
$$=1$$

RHS

$$=1-(\sec ^{2}x+\sec ^{2}x)$$
$$=1+\sec ^{2}x-\sec ^{2}x$$
$$=1$$

Are these steps correct?

harsimran_hs4 · Answer

no these are not correct
look above at my post i have done all the steps

anonymous · Answer

im not sure how you came up with this = = sec^4 x + 1 - 2sec^2 x

harsimran_hs4 · Answer

(a+b)^2 = a^2 + b^2 +2ab 
clear, if not think a little about it`s proof