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Prove that (sqrt(3)+1)(3-cot30^@)=tan^3(...

Prove that `(sqrt(3)+1)(3-cot30^@)=tan^3(60)^@-2sin60^@`

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RHS= `tan^(3)60^(@)-2sin60^(@)=(sqrt(3))^(2) - 2sqrt(3)/2=3sqrt(3)-sqrt(3)=2sqrt(3)`
LHS`=(sqrt(3)+1)(3-cot30^(@))=(sqrt(3)+1)(3-sqrt(3))`
`therefore tan60^(2)=sqrt(3)sin60^(@)=sqrt(3)/2` and `=(sqrt(3)+1)sqrt(3)(sqrt(3)-1) cot 30^(@)=sqrt(3)`
`=sqrt(3)(sqrt(3))^(2)-1) = sqrt(3)(3-1)=2sqrt(3)`
`therefore` LHS = RHS Hence proved.
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NCERT EXEMPLAR-INTRODUCTION TO TRIGoNOMETRY AND ITS APPLICATIONS-Introduction To Trigonometry And Its Applications
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  2. (sinalpha + cosalpha)(tanalpha + cotalpha) = secalpha + cosecalpha

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  3. Prove that (sqrt(3)+1)(3-cot30^@)=tan^3(60)^@-2sin60^@

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  4. Show that 1+cot^2alpha/(1+cosecalpha)=cosec alpha

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  6. Find the angle of elevation of the Sun when the shadow of a pole h m ...

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  7. If sqrt(3)tantheta=1 then find value of sin^2theta-cos^2theta

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  9. Simplify: (1+tan^(2)theta)(1-sintheta)(1+sintheta)

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  10. If 2sin^2theta-cos^2theta=2, find the value of theta.

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  11. Evaluate : (cos^2(45 + theta) + cos^2(45 - theta))/(tan(60^@ + theta)...

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  13. Prove the following identity: sec^4theta-sec^2theta=tan^4theta+tan^2th...

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  14. If cosectheta + cottheta=p, then cos theta=

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  15. Prove that sqrt(sec^(2)theta + cosec^(2)theta) = tantheta + cottheta.

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  16. The angle of elevation of the top of a tower from a certain point is 3...

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  17. If 1+sin^(2)theta = 3sinthetacostheta, then prove that tantheta=1 or 1...

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