Question

secA+tanA=m,then sec⁴A-tan⁴A-2secA.tanA​

Answer 1

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secA+tanA=m,then sec⁴A-tan⁴A-2secA.tanA

$\huge{\orange{\underline{\red{\mathscr{ANSWER:-}}}}}$

=(sec² a + tan² a)(sec2 a - tan2a) - 2sec a tan a

=sec² a + tan² a - 2sec a tan a

=(sec a - tan a)²

now,

We know that,

sec² a - tan² a = 1

=(sec a - tan a) (sec a + tan a)=1

=(sec a - tan a) (m) = 1

=(sec a - tan a)=1/m

on square both sides,

=(sec a - tan a)²= 1/m²

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