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Introduction to Trigonometry

Short Answer Type

331. Prove that: (1+cotA-cosecA) (1+tanA+secA) = 2

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332. Prove that: (sinθ + cosecθ)² + (cosθ + secθ)² = 7 + tan2θ + cot2θ.

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333. Prove that: sinθ (1+tanθ) + cos θ (1+cotθ) = secθ + cosecθ

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334.

If $7 space sin squared straight theta space plus space 3 space cos squared straight theta space equals space 4.$ Show that $tanθ space equals space fraction numerator 1 over denominator square root of 3 end fraction$

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335.
Prove that $fraction numerator cosθ minus sinθ plus 1 over denominator cosθ plus sinθ minus 1 end fraction equals cosecθ plus cotθ$

Solution not provided.

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336.

Prove that: $open parentheses cosecθ minus sinθ close parentheses space left parenthesis sinθ minus cosθ right parenthesis space equals space fraction numerator 1 over denominator tanθ plus cotθ end fraction$

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337.

Prove that: $fraction numerator cosecA over denominator cosecA minus 1 end fraction plus fraction numerator cosecA over denominator cosecA plus 1 end fraction equals 2 sec squared straight A$

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338.

Prove that: $fraction numerator 1 over denominator secA plus tanA end fraction minus 1 over cosA equals 1 over cosA minus fraction numerator 1 over denominator secA minus tanA end fraction$

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339.

If $sinθ equals 1 third comma$ find the value of (2 cot² θ = 2).

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340.

Simplify: $fraction numerator sin cubed straight theta plus cos cubed straight theta over denominator sinθ plus cosθ end fraction plus sinθ. space cosθ$

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Previous Year Papers

Test Series

Test Yourself

Short Answer Type

335. Prove that

335.
Prove that $fraction numerator cosθ minus sinθ plus 1 over denominator cosθ plus sinθ minus 1 end fraction equals cosecθ plus cotθ$