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What is the value of sin^2theta+1/(1+...

What is the value of `sin^2theta+1/(1+tan^2theta)` ?

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The correct Answer is:
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`(sin^(2)theta+(1)/(1+tan^(2)theta))=(sin^(2)theta+(1)/(sec^(2)theta))=(sin^(2)theta+cos^(2)theta)=1.`
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RS AGGARWAL-TRIGONOMETRIC IDENTITIES-Exercise 13C
  1. Write the value of (1+tan^(2)theta)cos^(2)theta.

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  2. Write the value of (1+cot^(2)theta)sin^(2)theta.

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  3. What is the value of sin^2theta+1/(1+tan^2theta) ?

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  4. Write the value of cot^2theta-1/(sin^2theta) .

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  5. Write the value of sintheta cos(90^(@)-theta)+costheta sin(90^(@)-the...

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  6. Write the value of "cosec"^(2)(90^(@)-theta)-tan^(2)theta.

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  7. Write the value of sec^(2)theta(1+sin theta)(1-sin theta).

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  8. Write the value of "cosec"^(2)theta(1+costheta)(1-costheta).

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  9. Write the value of sin^(2)theta cos^(2)theta(1+tan^(2)theta)(1+cot^(2...

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  10. Smlplify : (1+tan^(2)theta)(1-sintheta)(1+sintheta)

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  11. Write the value of 3 cot^(2)theta - 3 "cosec"^(2)theta.

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  12. Write the value of 4 tan^(2)theta-(4)/(cos^(2)theta).

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  13. Write the value of (tan^(2)theta-sec^(2)theta)/(cot^(2)theta-"cosec...

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  14. If sin theta=(1)/(2), " write the value of " (3cot^(2)theta+3).

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  15. If cos theta=(2)/(3), " write the value of " (4+ 4 tan^(2)theta).

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  16. If cos theta=(7)/(25), " write the value of " (tan theta + cot theta)...

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  17. If cos theta = (2)/(3), " write the value of " ((sectheta-1))/((secth...

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  18. If 5 tan theta =4, " write the value of " ((costheta- sintheta ))/((c...

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  19. If 3 cot theta =4, " write the value of " ((2costheta+ sintheta ))...

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  20. If cottheta=1/(sqrt(3)) , show that (1-cos^2theta)/(2-sin^2theta)=3...

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