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sec4θsec2θsec ^{4} heta-sec ^{2} heta is equal to

a

tan2 T + tan4 T

b

cos4 T – cos2 T

c

tan2 T – tan4 T

d

cos2 T – cos4 T

Answer : Option A
Explanation :

sec4θsec2θsec ^{4} heta-sec ^{2} heta

=sec2θ(sec2θ1)=sec ^{2} hetaleft(sec ^{2} heta-1 ight)

=(1+tan2θ)(1+tan2θ1)=left(1+ an ^{2} heta ight)left(1+ an ^{2} heta-1 ight)

=tan2θ+tan4θ= an ^{2} heta+ an ^{4} heta

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