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Introduction to Trigonometry

Short Answer Type

271. If cot θ + tan θ = x and sec θ – cos θ = y, prove that (x²y)^2/3 – (xy²)^2/3 = 1.

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272. If sin θ + sin² θ = 1. Prove that cos² θ + cos² θ = 1

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273. If 3 sin θ + 5 cos θ = 5, prove that 5 sin θ – 3 cos θ = ± 3.

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274.
Prove $fraction numerator cos cubed straight theta plus sin cubed straight theta over denominator cosθ plus sinθ end fraction plus fraction numerator cos cubed straight theta minus sin cubed straight theta over denominator cosθ minus sinθ end fraction equals 2.$

Solution not provided.

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275. In the given Fig. ABC is a right angled triangle. D is the mid-point of B. Show that

tanθ over tanφ equals 1 half.

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276.

Prove that: $fraction numerator sinθ over denominator secθ plus tanθ minus 1 end fraction plus fraction numerator cosθ over denominator cosecθ plus cotθ minus 1 end fraction equals 1.$

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277. If a cos³ θ + 3 a cos θ. sin² θ = m and a sin³ θ + 3a cos² θ.sin θ = n, then prove that

left parenthesis straight m plus straight n right parenthesis to the power of 2 divided by 3 end exponent plus left parenthesis straight m minus straight n right parenthesis to the power of 2 divided by 3 end exponent space equals space 2 straight a to the power of 2 divided by 3 end exponent.

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278. Evaluate: tan 35°. tan 40°. tan 45°. tan 50°. tan 55°.

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279. Show that:

open parentheses cosecθ minus sinθ close parentheses space left parenthesis secθ. space cosθ right parenthesis space equals space fraction numerator 1 over denominator tanθ plus cotθ end fraction.

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280. Show that

fraction numerator sinθ minus 2 sin cubed straight theta over denominator 2 space cos cubed straight theta minus cosθ end fraction space equals space tanθ.

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Previous Year Papers

Test Series

Test Yourself

Short Answer Type

274. Prove

274.
Prove $fraction numerator cos cubed straight theta plus sin cubed straight theta over denominator cosθ plus sinθ end fraction plus fraction numerator cos cubed straight theta minus sin cubed straight theta over denominator cosθ minus sinθ end fraction equals 2.$