If-tan-2-1-x-2-then-prove-that-sec-tan-3-cosec-2-x-2-3-

Question Number 206434 by MATHEMATICSAM last updated on 14/Apr/24

If \tan^{2} θ = 1 - x^{2} then prove that

\sec θ + \tan^{3} θ cosec θ = \sqrt{{(2 - x^{2})}^{3}} .

Answered by TonyCWX08 last updated on 14/Apr/24

s e c θ + {t a n}^{3} θ (\frac{s e c θ}{t a n θ})

= s e c θ + s e c θ {t a n}^{2} θ

= s e c θ (1 + 1 - x^{2})

= \sqrt{(1 + {t a n}^{2} θ)} (2 - x^{2})

= \sqrt{(2 - x^{2})} (2 - x^{2})

= \sqrt{{(2 - x^{2})}^{3}}

H e n c e P r o v e d .