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Evaluate : tan35^0tan40^0tan45^0tan50...

Evaluate : `tan35^0tan40^0tan45^0tan50^0tan55^0`

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To evaluate the expression \( \tan 35^\circ \tan 40^\circ \tan 45^\circ \tan 50^\circ \tan 55^\circ \), we can use the properties of trigonometric functions, particularly the relationship between tangent and cotangent. ### Step-by-Step Solution: 1. **Identify the angles**: We have the angles \( 35^\circ, 40^\circ, 45^\circ, 50^\circ, \) and \( 55^\circ \). 2. **Use the identity**: Recall that \( \tan(90^\circ - \theta) = \cot(\theta) \). This means: - \( \tan 50^\circ = \cot 40^\circ \) ...
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RD SHARMA-TRIGONOMETRIC RATIOS-All Questions
  1. Evaluate : 4(sin^4 30^0+cos^4 60^0)-2/3(sin^2 60^0-cos^2 45^0)+1/2tan...

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  2. Evaluate : (sin50^0)/(cos40^0)+(cos e c40^0)/(sec50^0)-4cos50^0cos e ...

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  3. Evaluate : tan35^0tan40^0tan45^0tan50^0tan55^0

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  4. Evaluate : cos e c(65^0+theta)-sec(25^0-theta)-tan(55^0-theta)+cot(...

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  5. Evaluate : tan7^0tan23^0tan60^0tan67^0tan83^0

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  6. Evaluate : (2sin68^0)/(cos22^0)-(2cot15^0)/(5tan75^0)-(3tan45^0tan20^...

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  7. Evaluate : ((3cos55^0) / (7sin35^0))-(4/7)(cos70^0cos e c20^0)/(tan5^0...

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  8. Prove the following: (cos(90^0-theta)sec(90^0-theta)t a ntheta)/(cos ...

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  9. Prove the following: (tan(90^0-A)cotA)/(cos e c^2A)-cos^2A=0

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  10. Prove the following: sinthetasin(90^0-theta)-costhetacos(90^0-theta)=...

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  11. In a /\A B C , right angled at B , if A B=4 and B C=3 , find all t...

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  12. In a /\A B C , right angled at B , if A B=12 and B C=5 , find: (i) ...

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  13. If sinA=3/5 , find cosA and tanA .

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  14. If costheta=8/(17) , find the other five trigonometric ratios.

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  15. In a right triangle A B C right angled at B, if sinA=3/5 , find a...

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  16. If sinA=1/3, evaluate cosA\ cosec\ A+tanAsecA.

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  17. In a right triangle A B C , right angled at C , if tanA=1 , then...

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  18. If secalpha=5/4, evaluate (1-tanalpha)/(1+tanalpha).

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  19. If sintheta=1/2, show that (3costheta - 4cos^3theta)=0

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  20. If tanA=2 , evaluate secAsinA+tan^2A-cos e c\ A .

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