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Introduction to Trigonometry

Short Answer Type

341. Find the value of sin 30° geometrically.

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342. Without using trigonometric table, evaluate:

fraction numerator cos space 58 degree over denominator sin space 32 degree end fraction plus fraction numerator sin space 22 degree over denominator cos space 68 degree end fraction minus fraction numerator cos space 38 degree. space cosec 32 degree over denominator tan 18 degree. tan 35 degree. space tan 60 degree. space tan space 72 degree. tan 55 degree end fraction

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343. If sec² θ = (1 + sin θ) (1 – sin θ) = k, then find the value of k.

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344.

If $cot space straight theta space equals space 15 over 8 comma$ then evaluate $fraction numerator left parenthesis 2 plus 2 sinθ right parenthesis space left parenthesis 1 minus sinθ right parenthesis over denominator left parenthesis 1 plus cosθ right parenthesis space left parenthesis 2 minus 2 cosθ right parenthesis end fraction$

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345. Find the value of tan 60°, geometrically.

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346. Evaluate:

2 over 3 cosec squared 58 degree minus 2 over 3 cot space 58 degree. space tan space 32 degree minus 5 over 3 space tan space 13 degree. space tan 37 degree. space tan space 45 degree. tan 53 degree. space tan 77 degree.

find the value of cosec B.

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347.
If $secA space equals space 15 over 7 space and space straight A plus straight B space equals space 90 degree comma$ find the value of cosec B.

Solution not provided.
Ans. $15 over 7$

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348. Without using trigonometric tables, evaluate:

fraction numerator 7 space cos space 70 degree over denominator 2 space sin space 20 degree end fraction plus 3 over 2 fraction numerator cos space 55 degree. space cosec space 35 degree over denominator tan space 5 degree. space tan 25 degree. space tan 45 degree. space tan 85 degree. space tan space 65 degree end fraction

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349.

Prove that: $sec squared straight theta minus fraction numerator sin squared straight theta minus 2 sin to the power of 4 straight theta over denominator 2 cos to the power of 4 straight theta minus cos squared straight theta end fraction equals 1.$