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Evaluate cos thetasin theta + cos thet...

Evaluate
`cos thetasin theta + cos thetacos (90 - theta) + {(sin theta - sin (90 - theta)}^2`.

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KALYANI PUBLICATION-Complementary Angles and there Trigonamytry Ratios-EXERCISE
  1. Evaluate sec 50" sin 40° + cos 40" cosec 50°.

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  2. Evaluate sin theta sec (90 - theta) + cos theta cosec (90 - theta).

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  3. Evaluate cos thetasin theta + cos thetacos (90 - theta) + {(sin thet...

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  4. If sin 3 theta = cos (theta- 26°) where 3 theta and (theta -26°) are a...

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  5. If cot 5 theta = tan 10 theta, then find the value of theta.

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  6. If cos (20° + theta) = sin 30°, then find the value of theta.

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  7. If cos 9 theta = sin theta and 9 theta < 90° then find the value of ta...

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  8. If tan 2 theta = cot (theta - 18°), then the value of theta.

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  9. Prove that: tan 5° tan 85° tan 30° tan 65° tan 25° = 1/sqrt 3.

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  10. Prove that: tan 4° tan 43° tan 47° tan 86° = 1.

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  11. Prove that: tan 35° tan 40° tan 45° tan 50° tan 55° = 1.

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  12. Prove that: cosec (65° + theta) - sec (25° - theta) - tan (55° - the...

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  13. Prove that: (2 sin 68°)/(cos 22°)-( 2 cot 15°)/( 5 tan 75°)- 3( tan ...

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  14. Prove that: (cos^2 20° + cos^2 70°)/(sin^2 20° + sin^2 70°) +sin^2 6...

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  15. Prove that: (tan 50° + sec 50°)/(cot 40° + cosec 40°) + cos 40° cose...

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  16. In a ∆ ABC prove that sin( (A+B)/2) = COS (c/2).

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  17. In a ∆ ABC prove that cos ((A+B)/2) = sin (c/2).

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  18. In a ∆ ABC prove that tan( (A+B)/2) = cot( C/2).

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  19. In a ∆ ABC prove that sec^2 (B+C)/2 -1=cot^2 A/2.

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  20. If A +B = 90, prove that (cos A + cos B)/(sin A+ sinB)=1.

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