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P-2 Trigonometry — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsP-2 Trigonometry2 Marks
Question
Prove the following.
$tan^4\theta + tan^2\theta = sec^4\theta - sec^2\theta$
 
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Answer

Taking LHS
$tan^4\theta + tan^2\theta$
$= tan^2\theta ( tan^2\theta + 1)$
$= (sec^2\theta - 1)(sec^2\theta ) [1 + tan^2\theta = sec^2\theta ]$
$= sec^4\theta - sec^2\theta$
= RHS
Proved !

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