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For triangle ABC, show that : (i) "sin...

For triangle ABC, show that :
(i) `"sin" (A + B)/(2) = "cos" (C)/(2)`
(ii) `"tan" (B + C)/(2) = "cot" (A)/(2)`

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ICSE-TRIGONOMETRICAL IDENTITIES-EXERCISE 21 (C)
  1. Prove that : (sin A )/(sin (90^(@) -A)) + (cos A )/( cos (90^(@) - A )...

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  2. Show that : sin A cos A - (sin A cos(90^(@) - A) cos A)/ (sec (90^(@...

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  3. For triangle ABC, show that : (i) "sin" (A + B)/(2) = "cos" (C)/(2) ...

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  4. For triangle ABC, show that "tan"(B+C)/2="cot"A/2

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

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  6. Evaluate : 3 cos 80^(@)cosec 10^(@)+2sin 59^(@)sec 31^(@)

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  7. Evaluate : (sin 80^(@))/(cos 10^(@))+sin 59^(@)sec 31^(@)

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  8. Evaluate : tan (55^(@)-A)-cot (35^(@)+A)

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  9. Evaluate : cosec(65^(@)+A)-sec(25^(@)-A)

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  10. Evaluate : 2 (tan 57^(@))/(cot 33^(@))-(cot 70^(@))/(tan 20^(@))-sqr...

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  11. Evaluate : (cot^(2)41^(@))/(tan^(2)49^(@))-2(sin^(2)75^(@))/(cos^(2)...

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  12. Evaluate : (cos 70^(@))/(sin 20^(@))+(cos 59^(@))/(sin31^(@))-8sin^(...

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  13. Evaluate : 14 sin 30^(@)+6cos 60^(@)-5tan 45^(@)

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  14. A triangle ABC is right angled at B, find the value of (sec A . cose...

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  15. Find (in each case, given below) the value of x, if : sin x = sin 60...

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  16. Find (in each case, given below) the value of x, if : sin x = sin 60...

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  17. Find (in each case, given below) the value of x, if : cos x = cos 60...

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  18. Find (in each case, given below) the value of x, if : tan x = (tan 6...

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  19. Find (in each case, given below) the value of x, if : sin 2 x = 2 si...

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  20. Find (in each case, given below) the value of x, if : sin 3 x = 2 si...

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