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Prove that : (i) 1+(cos^(2)theta)/(si...

Prove that : (i) `1+(cos^(2)theta)/(sin^(2)theta)-"cosec"^(2)theta=0`
(ii) `(1+tan^(2)theta)/("cosec"^(2)theta)=tan^(2)theta`

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prove that: tan^(2) theta-cot^(2) theta=sec^(2) theta- cosec^(2) theta

Prove each of the following identities : (i) (sec^(2) theta -1) cot^(2) theta =1 " " (ii) (sec^(2) theta -1) ("cosec"^(2)theta -1) =1 (iii) (1- cos^(2) theta )sec^(2) theta = tan^(2) theta

(tan^(2)theta)/(tan^(2)theta-1)+(cosec^(2)theta)/(sec^(2)theta-cosec^(2)theta)=(1)/(sin^(2)theta-cos^(2)theta)

prove that tan^(2)theta+cot^(2)theta=sec^(2)theta+cosec^(2)theta-2

Prove each of the following identities : (i) 1+ (cot^(2) theta)/((1+ "cosec"theta))= "cosec" theta (ii) 1+ (tan^(2) theta)/((1+ sec theta))= sec theta

Prove that (cosec^(2)theta+sec^(2)theta)/(cosec^(2)theta-sec^(2)theta)=(1+tan^(2)theta)/(1-tan^(2)theta)

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NAGEEN PRAKASHAN-INTRODUCTION TO TRIGONOMETRY-Exercise 8 C
  1. Prove that : (i) (1)/(1+tan^(2)theta)+(1)/(1+cot^(2)theta)=1 ...

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  2. If costheta=(15)/(17), then find the value of sintheta.

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  3. Prove that : (i) 1+(cos^(2)theta)/(sin^(2)theta)-"cosec"^(2)theta=0...

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  4. Prove that 1+tan^2A/(1+secA)=secA

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  5. Prove that : (cotA-1)/(2-sec^(2)A)=(cotA)/(1+tanA)

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  6. tan^(2)theta+cot^(2)theta+2=sec^(2)theta cosec^(2)theta

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  7. Prove that : (tanA+cotA)^(2)=sec^(2)A+"cosec"^(2)A

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  8. Prove that : (sec^(2)A-1)("cosec"^(2)A-1)=1

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  9. Prove the following identities: cosec^4A-sec^2A=tan^4A+tan^2A

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  10. Prove that : (i) tan^(2)A-sin^(2)A=tan^(2)A*sin^(2)A (i...

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  11. Prove that : (1-tan^(2)theta)/(cot^(2)theta-1)=tan^(2)theta

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  12. Prove that : (sectheta-tantheta)^(2)=(1-sintheta)/(1+sintheta)

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  13. Prove that : sec^(2)theta+"cosec"^(2)theta=sec^(2)theta*"cosec" ^(2)t...

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  14. Prove that : (sinA+cosA)^(2)+(sinA-cosA)^(2)=2

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  15. Prove that : sin^(4)theta-cos^(4)theta=2sin^(2)theta-1

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  16. Prove that : (i) (1-cosA)/(sinA)=(sinA)/(1+cosA) (ii) ...

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  17. Prove that : (1+sintheta)/(costheta)+(costheta)/(1+sintheta)=2secthe...

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  18. Prove that : (1-costheta)/(sintheta)+(sintheta)/(1-costheta)=2"cosec...

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  19. Prove that : (i) (1)/(1-cosA)+(1)/(1+cosA)=2"cosec"^(2)A " " (...

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  20. Prove that : (i) (1)/(sectheta-tantheta)+(1)/(sectheta+tantheta)=2se...

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