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Mathematics : Introduction to Trigonometry

Short Answer Type

321. Without using trignometric tables, evaluate the following:

fraction numerator cosec squared 65 degree minus tan squared 25 degree over denominator sin squared 17 degree plus sin squared 73 degree end fraction plus fraction numerator 1 over denominator square root of 3 end fraction left parenthesis tan space 10 degree. space tan space 30 degree. space tan space 80 degree. right parenthesis

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322. Without using trignometric tables, evaluate the following:

2 open parentheses fraction numerator cos 58 degree over denominator sin 32 degree end fraction close parentheses minus square root of 3 open parentheses fraction numerator cos 35 degree. space cosec 52 degree over denominator tan space 15 degree. space tan 60 degree. space tan 75 degree end fraction close parentheses

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323. If sin3θ = cos (θ–6°) and 3θ and θ–6° are acute angles, find the value of θ.

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324.

If $3 space cotθ space equals space 4 comma$ find the value of $fraction numerator 5 space sin space straight theta space minus space 3 space cos space straight theta over denominator 5 space sinθ space plus space 3 space cosθ end fraction.$

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325.

If $tanA space equals space 5 over 12 comma$ find the value of $left parenthesis sinA plus cosA right parenthesis space secA.$

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326. If sec4A = cosec (A - 20) where 4A is an acute angle, find the value of A.

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327. In a ΔABC, right angled at C, if

tanA space equals space fraction numerator 1 over denominator square root of 3 end fraction comma

find the value of sinA.cosB+cosA.sinB.

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328. If sec2A = cosec (A - 42)where 2A is an acute angle, find the value of A.

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329. In ΔABC, right angled at A, if

tanC space equals space square root of 3 comma

find the value of sinB.cosC+cosB sinC.

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330.

Prove that: $fraction numerator cotA minus cosA over denominator cotA plus cosA end fraction equals fraction numerator cosecA minus 1 over denominator cosecA plus 1 end fraction$

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