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Prove that 3sinpi/6secpi/3-4sin(5pi)/6co...

Prove that `3sin``pi/6``sec``pi/3``-4sin``(5pi)/6``cot``pi/4``=1`

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`L.H.S = 3sin(pi/6)sec(pi/3)-4sin(5pi/6)cot(pi/4)`
`=3(1/2)(2)-4sin(pi-(pi/6))(1)`
As we know, `sin(pi -x) = sinx`
Our equation becomes,
`=3(1/2)(2)-4sin(pi/6)(1)`
`=3-4(1/2) = 1 = R.H.S.`
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NCERT-TRIGONOMETRIC FUNCTIONS-SOLVED EXAMPLES
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  2. The minute hand of a watch is 1.5 cm long. How far does its tip move ...

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  3. If the arcs of the same lengths in two circles subtend angles 65 ^cir...

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  4. Convert 6 radians into degree measure.

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  5. Find the radius of the circle in which a central angle of 60^@interce...

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  6. Convert 40^circ 20^(prime)into radian measure.

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  7. Find the principal solution of the equation tanx=-1/(sqrt(3)).

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  8. Find the principal solution of the equation sinx=(sqrt(3))/2.

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  9. Find the value of sin\ 15^circ.

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  10. Prove that 3sinpi/6secpi/3-4sin(5pi)/6cotpi/4=1

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  11. Prove that (sin(x+y))/(sin(x-y))=(tanx+tany)/(tanx-tany)

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  12. Find the value of tan\ (13pi)/(12).

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  13. Prove that cos(pi/4+x)+cos(pi/4-x)=sqrt(2)cosx.

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  14. Show that tan 3x tan 2x tan x = tan 3x - tan 2x - tan x.

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  15. Prove that (sin5x-2sin3x+sinx)/(cos5x-cosx)=tanx

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  16. Prove that (cos7x+cos5x)/(sin7x-sin5x)=cotx.

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  17. In triangle ABC , prove that tan (B-C)/2 =[( b-c) /(b+c )] cot A/2 , ...

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  18. The angle of elevation of to be top point P of the vertical tower PQ o...

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  19. Prove that asin(B−C)+bsin(C−A)+csin(A−B)=0

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  20. In triangle ABC, prove thattan(B-C)/2=(b-c)/(b+c)cotA/2tan(C-A)/2=(c-a...

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