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Multiple Choice Questions
1. $$sec^4 θ - sec^2 θ$$ is equal to
(A): $$tan^2 θ - tan^4 θ$$
(B): $$tan^2 θ + tan^4 θ$$
(C): $$cos^4 θ - cos^2 θ$$
(D): $$cos^2 θ - cos^4 θ$$
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By: anil on 05 May 2019 01.58 am
$$sec^4 θ - sec^2θ$$ = $$frac{1}{cos^4 θ} - frac{1}{cos^2 θ}$$
$$frac{1}{cos^4θ} - frac{1}{cos^2θ}$$= $$frac{1 - cos^2θ}{cos^4θ}$$
$$frac{1 - cos^2θ}{cos^4θ} = frac{sin^2θ}{cos^4θ}$$
$$ frac{sin^2θ}{cos^4θ} = tan^2θ imes sec^2θ $$
$$ tan^2θ imes sec^2θ $$ = $$tan^2 θ imes $$ $$ (tan^2 +1)$$ $$tan^2 θ imes $$ $$ (tan^2 +1)$$ = $$tan^2 θ + tan^4 θ $$
Hence Option B is the correct answer.
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SSC CGL 2012 Tier 1 1 July NZ Morning III
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$$frac{1}{cos^4θ} - frac{1}{cos^2θ}$$= $$frac{1 - cos^2θ}{cos^4θ}$$
$$frac{1 - cos^2θ}{cos^4θ} = frac{sin^2θ}{cos^4θ}$$
$$ frac{sin^2θ}{cos^4θ} = tan^2θ imes sec^2θ $$
$$ tan^2θ imes sec^2θ $$ = $$tan^2 θ imes $$ $$ (tan^2 +1)$$ $$tan^2 θ imes $$ $$ (tan^2 +1)$$ = $$tan^2 θ + tan^4 θ $$
Hence Option B is the correct answer.