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Show that 2(cos^(4)60^(@)+sin^(4)30^(@...

Show that
`2(cos^(4)60^(@)+sin^(4)30^(@))-(tan^(2)60^(@)+cot^(2)45^(@))+3sec^(2)30^(@)=1/4`

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The correct Answer is:
`1/4`
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Evaluate the following (sec^(2) 60^(@) -tan ^(2) 60^(@) )/( sin ^(2) 30^(@) +cos ^(2) 30^(@) )

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Show that cos(2"tan"^(-1)1/7)=sin(4"tan"^(-1)1/3) .

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KUMAR PRAKASHAN-INTRODUCTION TO TRIGONOMETRY-Other Important Examples
  1. Evaluate each of the following : tan60^(@)cosec^(2)45^(@)+sec^(2)60^...

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  2. Evaluate each of the following : 3cos^(2)30^(@)+sec^(2)30^(@)+2cos0^...

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  3. Show that 2(cos^(4)60^(@)+sin^(4)30^(@))-(tan^(2)60^(@)+cot^(2)45^(@...

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  4. Find the value of x in the following equation sin 2x = sin 60° cos 30°...

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  5. If theta is an acute angle and tan theta + cot theta = 2 , find the va...

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  6. Given that sin (A+ B) = sin A cos B + cos A sin B , find the value o...

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  7. Prove that : (cos80^(@))/(sin10^(@))+cos59^(@)cosec31^(@)=2

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  8. Evaluate the following : (2tan53^(@))/(cot37^(@))-(cot80^(@))/(tan10...

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  9. Express sin 72° + cot 72° in terms trigonometric ratios of angles betw...

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  10. Evaluate: ((sin47^(@))/(cos43^(@)))^(2)+((cos43^(@))/(sin47^(@)))^(2)-...

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  11. If sec 5A = cosec (A + 36°) , where 5A is an acute angle, find the va...

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  12. Prove the following : (All angles are acute angles.) sqrt(sec^(2)the...

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  13. Prove the following : (All angles are acute angles.) (1+tan^(2)theta...

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  14. Prove the following : (All angles are acute angles.) (tantheta+sinth...

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  15. Prove the following : (All angles are acute angles.) (sintheta+costh...

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  16. Prove the following : (All angles are acute angles.) tantheta-cotthe...

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  17. If sintheta + sin^(2)theta = 1 , prove that cos^(2)theta + cos^(4)thet...

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  18. If cos theta + sin theta = p and sec theta + cosec theta = q , prove t...

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  19. If costheta + sin theta = sqrt2 cos theta, prove that cos theta - sin ...

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  20. Prove that 2 (sin^(6)theta +cos^(6) theta ) - 3(sin^(4)theta +cos^(4...

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