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In the triangle ABC , in which C is the ...

In the triangle ABC , in which C is the right angle, prove that :
` sin 2 A =(2 ab )/(c ^(2)) , cos 2 A= ( b ^(2) - a ^(2))/( c ^(2)), sin ""(A)/(2) = sqrt ((c -b)/( 2c)) , cos ""(A)/(2)= sqrt ((c +b)/( 2c)).`

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ICSE-COMPOUND AND MULTIPLE ANGLES -EXERCISE 5 (C )
  1. Derive function of 120^(@) from functions of 60^(@) and check by usi...

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  2. If sin theta =a and sin 2 theta = b, find an expression for cos theta...

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  3. Given that tan A = (1)/(5). find the values of tan 2 A, tan 4A and ta...

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  4. If A is an obtuse angle whose sine is (5)/(13) and B is an acute ang...

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  5. Express cos 6 alpha in terms of cos 3 alpha .

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  6. sin 100 in terms of functions of 5 theta ,

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  7. write tan 8 alpha in temrs of tan 4 alpha .

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  8. cos 2 theta in terms of cos 4 theta,

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  9. tan 4 phi in terms of cos 8phi,

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  10. Express sin "" (5pi)/(2) in terms of cos 5pi ,

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  11. cos 20 theta in terms of sin 5 theta .

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  12. Using the half angle formulas, find the exact value of (i) sin 15 ^(@)...

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  13. In the triangle ABC , in which C is the right angle, prove that : s...

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  14. If cos alpha = (3)/(5) , cos beta = (4)/(5) , find the value of cos ...

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  15. Given that cos ""(A)/(2) = (12)/(13), calculate without the use of tu...

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  16. Given that tan x = (12)/(5), cos y = (-3)/(5), and the angles x and y ...

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  17. Given that sin ^(2) beta = sin alpha cos alpha, show that cos 2 beta...

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  18. Derive formulas for the following in terms of functions of 2 theta an...

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  19. If sin alpha = 3/5, find value of (i) sin 3 alpha , (ii) cos 3 alpha ...

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  20. If 2 cos theta = x + (1)/(x), prove that 2 cos 3 theta = x ^(3) + (1...

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