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If tan A = n tan B and sin A = m sin B...

If
`tan A = n tan B and sin A = m sin B,`
prove that :
`cos^(2) A = (m^(2) - 1)/(n^(2) - 1)`

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ICSE-TRIGONOMETRICAL IDENTITIES-EXERCISE 21 (E)
  1. If x = a cos theta and y = bcot theta, show that : (a^(2))/(x^(2...

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  2. If sec A + tan A = p, show that : sin A = (p^(2) - 1)/(p^(2) + 1...

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  3. If tan A = n tan B and sin A = m sin B, prove that : cos^(2) A =...

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  4. if 2 sin A - 1 = 0, show that : sin 3 A = 3 sin A - 4 sin^(3) A

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  5. If 4 cos^(2) A - 3 = 0, show that : cos 3 A = 4 cos^(3) A - 3 co...

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  6. Evaluate without using trigonometric tables. 2(("tan" 35^(@))/("cot"...

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  7. Evaluate : sec 26^(@) sin 64^(@) + (cosec 33^(@))/(sec 57^(@))

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  8. Evaluate ( 5 sin 66 ^(@))/( cos 24 ^(@)) -( 2 cot 85^(@))/(tan 5^(@...

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  9. Evaluate cos 40 ^(@) cosec 50 ^(@)+ sin 50 ^(@) sec 40 ^(@)

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  10. Evaluate sin 27 ^(@) sin 63 ^(@) - cos 63^(@) cos 27 ^(@)

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  11. Evaluate : 3(sin 72^(@))/(cos 18^(@))-(sec 32^(@))/(cosec 58^(@))

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  12. Evaluate 3 cos 80 ^(@) cosec 10 ^(@) + 2 cos 59 ^(@) cosec 31 ^(@...

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  13. Evaluate : (cos 75^(@))/ (sin 15^(@)) + (sin 12^(@))/ (cos 78^(@)) -...

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  14. Prove that : tan (55^(@) + x) = cot (35^(@) - x)

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  15. Prove that : sec (70^(@) - 0) = cosec (20^(@) + 0)

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  16. Prove that : Sin( 28 ^(@) +A) = cos ( 62 ^(@) - A)

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  17. Prove that : (1)/ (1 + cos (90^(@) - A)) + (1)/ (1 - cos (90^(@) - A...

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  18. Prove that : (1)/ (1 + sin (90^(@) - A)) + (1)/ (1 - sin (90^(@) - A...

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  19. If A and B are complementary angles, prove that : cot B + cos B = se...

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  20. If A and B are complementary angles, prove that : cot A cot B - sin ...

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