Consider ΔACB, right-angled at C, in which AC = 4 units, BC = 3
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    Introduction to Trigonometry

    Multiple Choice QuestionsShort Answer Type

    151.

    If sin space straight A space equals space 1 half comma show that 3 space cosA space minus space 4 space cos cubed straight A space equals space 0.

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    152.

    If 3 space cot space straight theta space equals space 2 comma find the value of fraction numerator 4 space sin space straight theta space minus space 3 space cos space straight theta over denominator 2 space sin space straight theta space plus space 6 space cos space straight theta end fraction.

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    153.

    If tan space straight theta space equals space 4 over 5 comma find the value of fraction numerator 5 space sinθ space minus space 3 space cosθ over denominator 5 space sinθ space plus space 2 space cos space straight theta end fraction.

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    Answer

    Multiple Choice QuestionsLong Answer Type

    154.

    If sin space straight theta space equals space fraction numerator square root of 3 over denominator 2 end fraction comma find other trigonometric ratios.

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    Multiple Choice QuestionsShort Answer Type

    155.

    If tan space straight theta space equals space square root of 2 minus 1 comma show that sin space straight theta. space cos space straight theta space equals space fraction numerator square root of 2 over denominator 4 end fraction.

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    156. In right-triangle ABC, right angled at B, if cotA space equals space 4 over 3. Show that fraction numerator cos squared straight A minus sin squared straight A over denominator cos space straight A end fraction equals fraction numerator 1 minus tan squared straight A over denominator secA end fraction.
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    Multiple Choice QuestionsLong Answer Type

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    157. Consider ΔACB, right-angled at C, in which AC = 4 units, BC = 3 units and ΔABC = θ. Determine the values of:
     left parenthesis straight i right parenthesis space cos squared straight theta plus sin squared straight theta space as space equals space 1 left parenthesis ii right parenthesis space cos squared straight theta space minus space sin squared straight theta space as space equals space fraction numerator negative 7 over denominator 25 end fraction.

    Solution not provided.
    Ans. (i) 1,  (ii) fraction numerator negative 7 over denominator 25 end fraction

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    Multiple Choice QuestionsShort Answer Type

    158. In right-triangle ABC, right angled at B. If 3 tan A = 1, then verify that cosec2 A = 1 + cot2 A.
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    159. If ∠C and ∠R are acute angles such that sin C = sin R, then prove that ∠C = ∠R.
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    Multiple Choice QuestionsLong Answer Type

    160. Using the measurement given in the adjoining figure, find (i) cos θ, (ii) tan Φ, (iii) cosec Φ.
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