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If n is an integer, prove that, (ii) t...

If n is an integer, prove that,
(ii) `tan{(n pi)/2 + (-1)^(n) pi/4} = 1`

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CHHAYA PUBLICATION-TRIGONOMETRIC RATIOS OF ASSOCIATED ANGLES-EXERCISE - SHORT ANSWER TYPE QUESTIONS (4 marks)
  1. If tan theta = 15/8 and cos theta is negative, find the value of (sin ...

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  2. If theta lies in the fourth quadrant and "sec" theta = 5/3 then find t...

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  3. Find the sum of n terms: sin theta + sin(pi + theta) + sin (2pi + th...

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  4. If n is an integer, prove that, (i) cos(n pi + theta) = (-1)^(n) cos...

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  5. If n is an integer, prove that, (ii) tan{(n pi)/2 + (-1)^(n) pi/4} =...

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  6. If n is an integer, prove that, (iii) sin{n pi + (-1)^(n) cdot (pi)/...

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  7. If n is an integer, prove that, (iv) tan (n pi + alpha) = tan alpha

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  8. If A,B,C are the angles of a triangle, show that, (i) sin B cos(C +A...

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  9. If A,B,C are the angles of a triangle, show that, (ii) tan ((A - B)/...

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  10. If A,B,C are the angles of a triangle, show that, (iii) (cos A cos C...

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  11. If A,B,C are the angles of a triangle, show that, (iv) (tan(B + C) +...

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  12. If A, B, C, D are the four angle taken in order of a cyclic quadrilate...

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  13. If A, B, C, D are the four angle taken in order of a cyclic quadrilate...

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  14. If A, B, C, D are the four angle taken in order of a cyclic quadrilate...

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  15. If A, B, C, D are the four angle taken in order of a cyclic quadrilate...

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  16. Prove that, tan 1^(@) tan 2^(@) tan 3^(@).....tan 87^(@) tan 88^(@) ta...

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  17. Prove that, tan^(2) (pi/6) cdot tan^(2)(2pi/16) cdot tan^(2) (3pi/16) ...

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  18. Show that, tan 181^(@) tan182^(@) tan 183^(@).....tan 267^(@) tan 268^...

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  19. Prove that, cos^(2) (pi/4) + sin^(2) (3pi/4) + sin^(2) (5pi/4) + sin^(...

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  20. Find the minimum value of 2^(sin^2 theta) + 2^(cos^2 theta).

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