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Introduction to Trigonometry

Short Answer Type

301. Without using trigonometric table, evaluate:

cos space left parenthesis 40 degree plus straight theta right parenthesis minus sin left parenthesis 50 degree minus straight theta right parenthesis plus fraction numerator cos squared 40 degree plus cos squared 50 degree over denominator sin squared 40 degree plus sin squared 50 degree end fraction

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302.

Evaluate: $fraction numerator 2 space sin space 68 degree over denominator cos space 22 degree end fraction minus fraction numerator 2 space cot space 15 degree over denominator 5 space tan space 75 degree end fraction minus fraction numerator 3 space tan space 45 degree space tan space 20 degree space tan space 40 degree space tan space 50 degree space tan space 70 degree over denominator 5 end fraction$

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303.

Prove that: $fraction numerator tanθ over denominator 1 minus cotθ end fraction plus fraction numerator cot space straight theta over denominator 1 minus tanθ end fraction space equals space 1 plus tanθ plus cotθ.$

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304.
Evaluate:
$fraction numerator 3 space tan space 25 degree. space tan space 40 degree. space tan space 50 degree. space tan space 65 degree. space minus space begin display style 1 half end style tan squared 60 degree over denominator 4 left parenthesis cos squared 29 degree space plus space cos squared 61 degree right parenthesis end fraction$

Solution not provided.
Ans. $3 over 8$

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305.

Evaluate:
$fraction numerator sin space 70 degree over denominator cos space 20 degree end fraction plus fraction numerator cosec space 36 degree over denominator sec space 54 degree end fraction minus fraction numerator 2 space cos space 43 degree. space cosec space 47 degree over denominator tan space 10 degree. space tan space 40 degree. space tan space 50 degree. space tan space 80 degree end fraction.$

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306.

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

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307.

Evaluate: $fraction numerator secθ. space cosec space left parenthesis 90 degree minus straight theta right parenthesis space minus space tanθ. space cot space left parenthesis 90 degree minus straight theta right parenthesis plus sin squared 55 degree space plus space sin squared 55 degree over denominator tan space 10 degree. space tan space 20 degree. space tan space 60 degree. space tan space 70 degree. space tan space 80 degree end fraction$

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308.

Prove that: $fraction numerator sinθ plus cosθ over denominator sinθ minus cosθ end fraction plus fraction numerator sinθ minus cosθ over denominator sinθ plus cosθ end fraction equals fraction numerator 2 space sec squared straight theta minus 1 over denominator tan squared straight theta minus 1 end fraction.$

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309.

Evaluate:
$fraction numerator sec squared left parenthesis 90 degree minus straight theta right parenthesis minus cot squared straight theta over denominator 2 left parenthesis sin squared space 25 degree space plus space sin squared space 65 degree right parenthesis end fraction plus fraction numerator 2 cos squared space 60 degree. space tan squared space 28 degree. space tan to the power of 2 space end exponent 62 degree over denominator 3 space left parenthesis sec squared space 43 degree space minus space cot squared space 47 degree right parenthesis end fraction$

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310.

Prove that: $fraction numerator 1 plus cosθ over denominator 1 minus cosθ end fraction equals space left parenthesis cosecθ plus cotθ right parenthesis squared$

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Previous Year Papers

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Short Answer Type

304. Evaluate: