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If sin (alpha + beta) = 4/5 , sin (alpha...

If `sin (alpha + beta) = 4/5 , sin (alpha -beta) = (5)/(13), alpha + beta , alpha - beta` being acute angles prove that `tan 2 alpha = (63)/(16).`

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ICSE-COMPOUND AND MULTIPLE ANGLES -EXERCISE 5(A)
  1. Find the value of sin (alpha - beta), cos (alpha -beta) and tan (alph...

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  2. If A and B are acute angles, find (A+B) given sin A = (1)/(sqrt5) ,...

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  3. If A and B are acute angles, find (A+B) given tan A = (5)/(6), tan ...

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  4. Given that tan alpha = (m)/( m +1), tan beta = (1)/(2m +1) then what i...

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  5. In the Delta ABC the foot of the perpendicular from A to BC is D. Give...

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  6. Given that tan (A+ B) =1 and tan (A-B) = 1/7, find without using tab...

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  7. If tan (A +B) = x and tan B = 1/2 prove that tan A = (2 x -1)/(x +2) ...

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  8. If sin (alpha + beta) = 4/5 , sin (alpha -beta) = (5)/(13), alpha + be...

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  9. Prove that 1 + tan 2 theta tan theta = sec 2 theta .

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  10. Show that 4 sin ((pi)/(3) - theta ) sin ((pi)/(3) + theta) =3-4 sin ^(...

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  11. ( cos 17^(@) + sin 17^(@))/( cos 17^(@) - sin 17^(@)) = tan 62^(@)

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  12. tan 3A - tan 2 A - tan A = tan 3 A tan 2 A tan A.

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  13. tan 75 ^(@) - tan 30^(@)- tan 75^(@) tan 30^(@) =1.

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  14. Prove that cos 2 theta cos 2 phi + sin ^(2) ( theta - phi) -sin ^(2) (...

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  15. If sin (theta + alpha ) = cos ( theta + alpha), prove that tan theta ...

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  16. Given that A = B +C. prove that tan A - tan B - tan C = tan A tan B ...

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  17. If A +B = 45 ^(@), show that tan A + tan B + tan A tan B =1. Hence or ...

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  18. Use the expansion of tan (A-B) to find tan 15 ^(@) without the use o...

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  19. Prove that (2 tan A) /(1+ tan ^(2) A) = sin 2 A.

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  20. If A +B = 225 ^(@), prove that tan A + tan B =1- tan A tan B

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