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Prove the following identities: (sint...

Prove the following identities:
`(sintheta+costheta)(tantheta+cottheta)=sectheta+cosectheta`

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Prove the following identities : (sintheta-costheta+1)/(sintheta+costheta-1)=1/(sectheta-tantheta)

Prove the following identities : (cottheta+cosectheta-1)/(cottheta-cosectheta+1)=(1+costheta)/(sintheta)

Prove the following identities : 1/( sectheta-tantheta)-1/(costheta)=1/(costheta)-1/(sectheta+tantheta)

Prove the following identities: sqrt((1-costheta)/(1+costheta))=cosectheta-cottheta

Prove the following identities: (1+costheta+sintheta)/(1+costheta-sintheta)=(1+sintheta)/(costheta)

Prove the following identities: 1+(cot^(2)theta)/(1+cosectheta)=cosectheta

Prove the following identities : (cos^(3)theta+sin^(3)theta)/(costheta+sintheta)+(cos^(3)theta-sin^(3)theta)/(costheta-sintheta)=2

Prove the following identities : (tantheta+1/(costheta))^(2)+(tantheta-1/(costheta))^(2)=2((1+sin^(2)theta)/(1-sin^(2)theta))

Prove the following identities: tan^(2)theta+cot^(2)theta=sec^(2)thetacosec^(2)theta-2

Prove the following identities : (1+tan^(2)theta)/(1+cot^(2)theta)=((1-tantheta)/(1-cottheta))^(2)

KUMAR PRAKASHAN-INTRODUCTION TO TRIGONOMETRY-Practice Thoroughly
  1. If theta =45°, find the value of 2 cosec^(2)theta + 3 sec^(2)theta.

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  2. If tantheta=1/(sqrt3), find the value of sin (90^(@)-theta).

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  3. Find the value of cos^(2)15^(@)+cos^(2)25^(@)+cos^(2)65^(@)+cos^(2)7...

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  4. In DeltaPQR,angleP=60^(@),angleQ=90^(@) and PR=15cm. Find PQ.

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  5. Solve the equation for theta:(cos^(2)theta)/(cot^(2)theta-cos^(2)theta...

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  6. If tantheta+cottheta=2, find the value of tan^(2)theta+cot^(2)theta.

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  7. Express cos 63° + cot 59° - sec 47° in terms of trigonometric ratios o...

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  8. Given a right triangle ABC, right angled at B, in which tanA=15/8, fin...

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  9. If cottheta=15/8, find the value of (4cottheta-5sectheta-8cosectheta...

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  10. Prove the following identities: sqrt((1-costheta)/(1+costheta))=cos...

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  11. Prove the following identities: 1+(cot^(2)theta)/(1+cosectheta)=cos...

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  12. Prove the following identities : (tantheta+1/(costheta))^(2)+(tanthe...

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  13. Prove the following identities: (tan^(3)theta)/(1+tan^(2)theta)+(co...

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  14. Prove the following identities: tan^(2)theta+cot^(2)theta=sec^(2)th...

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  15. Prove the following identities: (1+tan^(2)theta)+(1+1/(tan^(2)theta...

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  16. Prove the following identities: (1+costheta+sintheta)/(1+costheta-s...

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  17. Prove the following identities: (sintheta+costheta)(tantheta+cotthe...

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  18. Prove the following identities: (cosA)/(1-tanA)+(sinA)/(1-cotA)=sin...

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  19. Prove the following identities : (tanA)/(secA-1)+(tanA)/(secA+1)=2co...

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