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Prove that:(tan(pi/4+x))/(tan(pi/4-x))=(...

Prove that:`(tan(pi/4+x))/(tan(pi/4-x))=((1+tanx)/(1-tanx))^2`

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It is known that `tan(A+B)= (tanA+tanB)/(1−tanAtanB)` ​
and` tan(A−B)= (tanA−tanB)/(1+tanAtanB)`
​ L.H.S.= `tan( pi/4−x)/tan(pi/4+x)
...
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NCERT ENGLISH-TRIGONOMETRIC FUNCTIONS-All Questions
  1. 2sin^2(pi/6 )+c o s e c^2((7pi)/6)cos^2(pi/3)=3/2

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  2. sin^2pi/6+cos^2pi/3-tan^2pi/4=-1/2

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  3. Prove that:(tan(pi/4+x))/(tan(pi/4-x))=((1+tanx)/(1-tanx))^2

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  4. Prove that:cos(pi/4-x)cos(pi/4-y)-sin(pi/4-x)sin(pi/4-y)=sin(x+y)

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  5. Find the value of : (i) sin75^o (ii) tan15^o

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  6. 2sin^2(3pi)/4+2cos^2pi/4+2sec^2pi/3=10

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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