Prove thatsec2 -11-cosec2 -1 -2 MARKS-

Formula: 1 Mark Application: 1 Mark (sec^2 θ 1)(1 cosec^2 θ) = (tan^2 θ)( cot^2 θ) = ( sin^2 θ/cos^2 θ ) ( cos^2 θ/sin^2 θ ) = 1 ...

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Trigonometric Ratios Using Right Angled Triangle

Prove thatsec...

Question

Prove that

$(s e c^{2} θ - 1) (1 - c o s e c^{2} θ) = - 1$ [2 MARKS]

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(i) s e c^{2} θ + c o s e c^{2} θ = s e c^{2} θ c o s e c^{2} θ

(i i) t a n^{2} θ - s i n^{2} θ = t a n^{2} θ s i n^{2} θ

(i i i) t a n^{2} θ + c o t^{2} θ + 2 = s e c^{2} θ c o s e c^{2} θ

(t a n θ + c o t θ)^{2} = s e c^{2} θ + c o s e c^{2} θ

\frac{c o s e c θ}{(c o s e c θ - 1)} + \frac{c o s e c θ}{(c o s e c θ + 1)} = 2 s e c^{2} θ

\sqrt{\frac{s e c θ - 1}{s e c θ + 1}} + \sqrt{\frac{s e c θ + 1}{s e c θ - 1}} = 2 c o s e c θ

\sqrt{{sec}^{2} θ + c o s e c^{2} θ} = tan θ + cot θ

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