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Exercise

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

Step-by-step Solution

Learn how to solve perfect square trinomial problems step by step online. Prove the trigonometric identity sec(x)^4-2sec(x)^2+1=tan(x)^4. Starting from the left-hand side (LHS) of the identity. The trinomial \sec\left(x\right)^4-2\sec\left(x\right)^2+1 is a perfect square trinomial, because it's discriminant is equal to zero. Using the perfect square trinomial formula. Factoring the perfect square trinomial.
Prove the trigonometric identity sec(x)^4-2sec(x)^2+1=tan(x)^4

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Final answer to the exercise

true

Try other ways to solve this exercise

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Similar Questions Solved

$tan\left(x\right)+cot\left(x\right)=sec\left(x\right)cosec\left(x\right)$

$\frac{1+\cos2x}{\sin2x}=\cot x$

$sec\left(x\right)-tan\left(x\right)sin\left(x\right)=\frac{1}{sec\left(x\right)}$

$\tan\left(x\right)+\cot\left(x\right)=\sec\left(x\right)\csc\left(x\right)$

$\tan\left(a\right)+\cot\left(a\right)=\sec\left(a\right)\csc\left(a\right)$

$\sec x-\sin x\tan x=\cos x$

$\frac{1-sin\left(x\right)}{cos\left(x\right)}=\frac{cos\left(x\right)}{1+sin\left(x\right)}$

Main Topic: Perfect Square Trinomial

Perfect Square Trinomials have first and last terms that are positive perfect squares. And the middle term is twice the product of the square roots of the first and third terms. The sign of the middle term will tell us whether the factorization will involve a binomial that is either a sum or a difference (signs need to match)

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