Find the value of\sec^4\theta– \tan^4\theta, if \sec^2\theta+ \tan^2\theta= 4 /15 .

SSC CPO SI and ASI Model Paper 10

Question : 127 of 200

Marks: +1, -0

Find the value of

sec^4θ– tan^4θ, if sec^2θ+ tan^2θ= 4 /15 .

Solution:

(1)

sec^2θ+ tan2θ= 4/15

sec^2θ– tan^2θ= 1

∴(sec^2θ+tan^2θ)(sec^2θ– tan^2θ)= 4/15

⇒sec^4θ– tan^4θ= 4/15

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