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(sintheta)/(1-cottheta)+(costheta)/(1-ta...

`(sintheta)/(1-cottheta)+(costheta)/(1-tantheta)` is equal to

A

`(1 - tan theta)/( 1 - cot theta) `

B

`(1 - cot theta)/(1 - tan theta)`

C

`cos theta + sin theta`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`(cos theta)/(1- tan theta)+ (sin theta)/(1-cot theta)`
` = (cos theta)/(1- (sin theta)/(cos theta)) + (sin theta)/(1- (cos theta)/(sin theta))`
` = ( cos^(2) theta)/(cos theta - sin theta)+ (sin^(2) theta)/(sin theta - cos theta)`
` (cos ^(2)theta)/(cos theta - sin theta) - (sin^(2) theta)/(cos theta - sin theta)`
` = (cos^(2) theta -sin^(2) theta)/(cos theta - sin theta)`
= ` ((cos theta + sin theta) (cos theta- sin theta))/( cos theta - sin theta) = cos theta + sin theta `
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-TRIGONOMETRIC FUNCTIONS -EXERCISE 2 (MISCELLANEOUS PROBLEMS)
  1. (sintheta)/(1-cottheta)+(costheta)/(1-tantheta) is equal to

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  2. If cosec theta =x + 1/(4x) then the value of cosec theta + cot theta...

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  3. If DeltaABC right angle at B, BC = 5 cm and AC -AB =1 cm. then (1 ...

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  4. If tan theta + cot theta =2, " then " tan^(2) theta + cot^(2) theta i...

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  5. If cos (81^(@) + theta) = sin(k/3 - theta) , then k is equal to

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  6. If sin theta = cos theta ,then the value of 2 tan^(2) theta + sin^(2)...

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  7. If tan x = sin45^(@) cos 45^(@) + sin 30^(@) then x is equal to

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  8. sin^(6) theta + cos^(6) theta is equal to

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  9. cos^(2)5^(@) +cos^(2)10^(@) + cos^(2) 15^(@) +…..+cos^(2) 85^(@) + cos...

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  10. (sin(90^(@) -theta)sin theta)/(tan theta) + sin^(2) theta is equal to

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  11. If tantheta=(20)/(21) , show that (1-sintheta+costheta)/(1+sintheta...

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  12. For 0 le theta le pi/2 the maximum value of sin theta + cos theta i...

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  13. (cos 70^(@))/(sin 20^(@)) + (cos 59^(@))/(sin 31^(@) ) - 8 sin^(2) 30^...

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  14. If sin theta = 1/2 and theta is acute then (3 cos theta -4 cos^(3) ...

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  15. If 3 sin theta + 4 cos theta =5 , then value of sin theta is

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  16. If theta "is theta " and (cos^(2)theta)/(cot^(2) theta -cos^(2) theta)...

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  17. The value of (1+cos (pi/6))(1+cos(pi/3))(1+cos ((2pi)/3))(1+cos((7pi...

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  18. If cos 20^(@) - sin 20^(@) =p " then " cos 40^(@) is equal to

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  19. If Sn=cos^ntheta+sin^n tehta then find teh value of 3S4-2S6

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  20. If cos x + cos^(2) x =1 then the value of sin^(12) x + 3 sin^(10)...

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  21. If x sin^3theta+ycos^3theta=sinthetacostheta and xsintheta=ycostheta ...

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