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

Prove that :
`(1)/ (1 + cos (90^(@) - A)) + (1)/ (1 - cos (90^(@) - A)) = 2 cosec^(2) (90^(@) - A)`

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Prove that : (sin A )/(sin (90^(@) -A)) + (cos A )/( cos (90^(@) - A )) = sec A cosec A.

Prove that : (cos (90^(@) - 0) cos 0) /(cot 0) = 1 - cos^(2) 0

Show that : sin A cos A - (sin A cos(90^(@) - A) cos A)/ (sec (90^(@) - A)) - (cos A sin (90^(@) - A) sin A)/ (cosec (90^(@) - A)) = 0

Prove the following identities : (1)/ (1 + cos A) + (1)/ (1 - cos A) = 2 cosec^(2) A

Prove that : sec ^(2) (90 ^(@) - theta) - (1)/(cot ^(2) ( 90 ^(@) - theta) )= 1

Prove that : (1)/ (cos A + sin A - 1) + (1)/ (cos A + sin A + 1) = cosec A + sec A

Prove that: ((1+ cos A)/(sin A))^(2)= (1 + cos A)/(1-cos A)

Prove that : (1 + cos A)/(1 - cos A) = (cosec A + cot A)^(2)

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ICSE-TRIGONOMETRICAL IDENTITIES-EXERCISE 21 (E)
  1. Prove that : sec (70^(@) - 0) = cosec (20^(@) + 0)

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

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

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

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

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

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  7. If A and B are complementary angles, prove that : cosec^(2) A + cose...

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  8. If A and B are complementary angles, prove that : (sin A + sin B)/ (...

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  9. Prove that : (1)/ (sin A - cos A) - (1)/ (sin A + cos A) = (2 cos A)...

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  10. Prove that : (cot^(2) A)/(cosec A - 1) - 1 = cosec A

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  11. Prove that : (cos A)/(1 + sin A) = sec A - tan A

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  12. Prove that : cos A (1 + cot A) + sin A (1 + tan A) = sec A + cosec A

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  13. Prove that : (sin A - cos A) (1 + tan A + cot A) = (sec A)/ (cosec^(...

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  14. Prove that : sqrt (sec^(2) A + cosec^(2) A) = tan A + cot A

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  15. Prove that : (sin A + cos A) (sec A + cosec A) = 2 + sec A cosec A

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  16. Prove that : (tan A + cot A) (cosec A - sin A) (sec A - cos A) = 1

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  17. Prove that : cot^(2) A - cot^(2) B = (cos^(2) A - cos^(2) B)/ (sin^(...

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  18. Prove that : (cot A - 1)/ (2 - sec^(2) A) = (cot A)/ (1 + tan A)

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  19. If 4 cos^(2) A - 3 = 0 and 0^(@) le A le 90^(@), then prove that :...

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

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