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Show that cos^(-1) ((cos alpha+cos beta)...

Show that `cos^(-1) ((cos alpha+cos beta)/(1+cosalpha cosbeta))=2 tan^(-1)(tan (alpha/2) tan (beta/2))`

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Show that cos^(-1)((cos alpha+cos beta)/(1+cos alpha cos beta))=2tan^(-1)(tan((alpha)/(2))tan((beta)/(2)))

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MARVEL PUBLICATION-TRIGONOMETRIC FUNCTIONS-HARDER SOLVED EXAMPLES
  1. If cos^(-1) x + cos^(-1) y + cos^(-1) z = pi" , prove that " x^(2) + ...

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  2. If cos^(-1)(x/a) + cos^(-1) (y/b) = alpha show that : (x^2)/(a^2) - (...

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  3. Prove that tan{(pi)/4 + 1/2 Cos^(-1)((a)/(b))}+tan{((pi)/4-1/2 Cos^(-1...

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  4. If 0<a1<a2<ddot<an , then prove that tan^(-1)((a1x-y)/(x+a1y))+tan^(-1...

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  5. If a(1), a(2), a(3),...., a(n) is an A.P. with common difference d, th...

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  6. If alpha = tan^(-1) ((xsqrt(3))/(2y - x)) and beta = tan^(-1) ((2x - y...

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  7. Find the period of the function f(x) = tan (3x + 5).

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  8. Find the period of (i) sin 3x + cos 3x

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  9. Find the period of sin 5x - cos 5x.

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  10. Find the period of the function f(x) = sin((pi x)/3) + cos ((pi x)/2...

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  11. If m tan(alpha-theta)/( cos^2 theta) = n (tan theta)/ (cos^2 (alpha -...

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  12. Show that cos^(-1) ((cos alpha+cos beta)/(1+cosalpha cosbeta))=2 tan^(...

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  13. tan[2.tan^(-1)(1/5)- pi/4]=

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  14. tan [cos^(-1)((4)/(5)) +tan ^(-1)((2)/(3))]=....

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  15. Solution of the equation tan^(-1)(2x) + tan^(-1)(3x) = pi/4

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  16. If sin^(-1)(x/5) + cosec^(-1) (5/4) = pi/2 , then the value of x is

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  17. cot[csc^(-1)(5/3) + tan^(-1)(2/3)] = ....

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  18. If x, y, z are in A.P. and tan^(-1) x, tan^(-1) y and tan^(-1)z are al...

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  19. If: tan^(-1) ((sqrt(1 + x^2)-1)/(x)) = 4 then : x =

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  20. If x != 0, then tan((pi)/4 + 1/2 cos^(-1) x) + tan ((pi)/4 - 1/2 cos...

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