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Prove that: cos((3pi)/2+x)cos(2pi+x)[cot...

Prove that: `cos((3pi)/2+x)cos(2pi+x)[cot((3pi)/2-x)+cot(2pi+x)]=1`

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`cos((3pi)/2)+x)cos(2pi+x)[cot((3pi)/2)-x)+cot(2pi+x)`
`=sinxcosx[tanx+cotx]`
`=sinxcosx((sinx/cosx)+(cosx+sinx))`
...
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NCERT ENGLISH-TRIGONOMETRIC FUNCTIONS-All Questions
  1. Find the value of : (i) sin75^o (ii) tan15^o

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  2. 2sin^2(3pi)/4+2cos^2pi/4+2sec^2pi/3=10

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  3. Prove that: cos((3pi)/2+x)cos(2pi+x)[cot((3pi)/2-x)+cot(2pi+x)]=1

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  4. Prove that: (cos(pi+x)cos(-x))/(sin(pi-x)cos(pi/2+x))=cot^2x

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  5. Find sinx/2,cosx/2 and tanx/2of the following : sin x =1/4,x in quadr...

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  6. Find the values of the trigonometric function cot(-(15pi)/4)

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  7. In a circle of diameter 40 cm. The length of a chord is 20 cm. Find t...

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  8. Find the degree measure of the angle subtended at the centre of a cir...

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  9. Find the angle in radian through which a pendulum swings if its lengt...

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  10. If in two circles, arcs of the same length subtend angles 60^@and 75^...

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  11. Find the radian measures corresponding to the following degree measur...

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  12. A wheel makes 360 revolutions in one minute. Through how many radians...

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  13. Find the degree measures corresponding to the following radian measur...

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  14. Prove that: sin 3x + sin 2x - sin x = 4 sin x cosx/2cos(3x)/2

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  15. Prove that: ((sin7x+sin5x)+(sin9x+sin3x))/((cos7x+cos5x)+(cos9x+cos3x)...

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  16. Prove that sinx + sin3x + sin5x+ sin7x=4cosxcos2xsin4x

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  17. Prove that: (cosx-cosy)^2+(sinx-siny)^2=4sin^2(x-y)/2

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  18. Prove that: (cosx+cosy)^2+(sinx-siny)^2=4cos^2(x+y)/2

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  19. Prove that: (sin 3 x +sin x) sin x + (cos 3x - cos x) cos x = 0

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  20. Prove that: 2cospi/(13)cos(9pi)/(13)+cos(3pi)/(13)+cos(5pi)/(13)=0

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