Important Questions of Introduction to Trigonometry Mathematics | Zigya

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 Multiple Choice QuestionsShort Answer Type

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251.

If secθ space equals space straight x plus fraction numerator 1 over denominator 4 straight x end fraction comma prove that secθ plus tanθ space equals space 2 space straight x space or space fraction numerator 1 over denominator 2 straight x end fraction.

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252.

Show that fraction numerator cosecθ plus cotθ over denominator cosecθ minus cotθ end fraction equals 1 plus 2 cot squared straight theta plus 2 cosecθ. space cotθ

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253. If x = y cos a. sin β, y = γ cos α.cos β, z = γ sin a. Show that x2 + y2 +z2 = γ2 = γ2.
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254.

If cosθ plus sinθ space equals space square root of 2 space cosθ comma show that cosθ minus sinθ space equals space square root of 2 space sin space straight theta.

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255. In the given Fig. ABCD is a rectangle with DC = 8 cm and BC = 6 cm. Line segment CM is drawn making an angle of 30° with DC, intersecting AD in M. Find the length of CM and DM.


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256. In the given Fig. ABCD is a rectangle in which segments AP and AQ are drawn as shown. Find the length of (AP + AQ).

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257.

If sin space straight theta plus space cos space straight theta space equals space square root of 2 space cos left parenthesis 90 degree minus straight theta right parenthesis. Determine cot space straight theta.

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258.

If tanθ space equals space 1 space space and space sinβ space equals space fraction numerator 1 over denominator square root of 2 end fraction. Find the value of cos (θ + β), if θ and β are both acute angles.

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259.

If fraction numerator cos space straight alpha over denominator cos space straight beta end fraction space equals space straight m space and space fraction numerator cos space straight beta over denominator sin space straight beta end fraction space equals space straight n comma show that left parenthesis straight m squared plus straight n squared right parenthesis space cos squared straight beta space equals space straight n squared.

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260. If x = a cos θ – b sin θ;   y = a sin θ + b cos θ. Prove that x2+ y2 = a2 + b2
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