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An angle theta is divided into two parts...

An angle `theta` is divided into two parts `alpha " and " beta` such that
`tan alpha : tan beta = x : y : " prove that ", sin (alpha - beta) =(x-y)/(x+y) sin theta.`

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CHHAYA PUBLICATION-TRIGONOMETRIC RATIOS OF COMPOUND ANGLES-Short Answer Type Questions
  1. Simplify: tan(pi/4 + theta) tan ((3pi)/4 + theta)

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  2. Simplify: sin (B + C) sin (B - C) + sin (C + A) sin (C - A) + sin(A ...

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  3. Find the expansion: sin (A - B + C)

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  4. Find the expansion: tan (A + B - C)

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  5. If sin alpha sin beta - cos alpha cos beta + 1 = 0,"show that", sin (a...

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  6. If A + B = 45^(@), "show that",(1 + tan A) (1 + tan B) = 2 , "hence fi...

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  7. If A + B + C = pi " and " cos A = cos B cos C, "show that" tan A = t...

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  8. If A + B + C = pi " and " cos A = cos B cos C, "show that" 2 cot B c...

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  9. An angle theta is divided into two parts alpha " and " beta such that ...

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  10. If tan theta = (Q sin alpha)/(P + Q cos alpha), "prove that", tan (alp...

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  11. If sin (alpha + beta) = n sin (alpha - beta) " and " n ne -1," prove t...

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  12. If cot alpha cot beta = 3,"show that", (cos (alpha - beta))/(cos (alph...

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  13. Find the value of (sin (alpha + beta))/(sin (alpha - beta)), "given th...

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  14. If 0^(@) < theta < 90^(@) "and" cos theta + sin theta = sqrt2,"find th...

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  15. If tan alpha = (x sin beta)/(1-x cos beta) " and " tan beta = (y sin a...

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  16. If tan theta + tan phi = x "and" cot theta + cot phi = y, "prove that ...

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  17. If tan theta = (2x - K)/(K sqrt3) " and " tan varphi = (xsqrt3)/(2 K-x...

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  18. If cos (theta - alpha) = p " and " sin(theta + beta) = q," show that "...

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  19. Eliminate theta " and " phi sin theta + sin phi = a, cos theta + co...

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  20. Eliminate theta " and " phi tan theta + tan phi = x, cot theta + co...

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