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Show that cos ^(4) alpha + 2 cos ^(2) al...

Show that `cos ^(4) alpha + 2 cos ^(2) alpha (1-(1)/(sec ^(2) alpha ))=(1- sin ^(4) alpha )`

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SRISIRI PUBLICATION-IPE SCANNER (TEXUAL BITS)-Very Short Questions (2 marks) (Trigonometric Ratios, Transformations)
  1. Prove that (1+cot theta -"cosec" theta ) (1+ tan theta + sec theta )=2...

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  2. If (2 sin theta )/(1+ cos theta + sin theta )=x, find the value of (1...

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  3. Show that cos ^(4) alpha + 2 cos ^(2) alpha (1-(1)/(sec ^(2) alpha ))=...

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  4. Prove that (tan theta + cot theta)^(2) = "sec"^(2) theta + "cosec"^(2)...

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  5. Prove that sin^(2)alpha + cos^(2) (alpha + beta) + 2 sin alpha sin bet...

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  6. If cos theta gt 0, tan theta + sin theta =m and tan theta -sin theta =...

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  7. For what values of x in the first quadrant (2 tan x)/( 1- tan ^(2) x) ...

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  8. If A, B, C are angles of a cyclic quadrilateral prove that cos A+ cos...

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  9. If A, B, C, D are angles of a cyclic quadrilateral then P.T sin A - s...

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  10. If alpha , beta are complementry angles such that bsin alpha = a, the ...

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  11. Find the expansion of sin(A+B+C).

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  12. Prove that sin ^(2) ((pi)/(8)+(A)/(2)) - sin ^(2) ((pi)/(8) - (A)/(2))...

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  13. Express cos^(6)A + sin^(6)A interms of sin 2A.

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  14. Simplify tan ((pi)/(4) +A) tan ((pi)/(4)-A)

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  15. Prove that tan 3A. tan2A.tanA = tan3A - tan 2A - tan A

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  16. Find tan 20^(@) + tan40^(@) + sqrt(3)tan20^(@)tan40^(@).

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  17. Prove that (sin theta + sin 2 theta )/(1+cos 0 + cos 2 theta )= tan th...

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  18. Express (1-costheta+sin theta)/(1+cos theta + sin theta) in terms of t...

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  19. Simplify (cot 55^(@)cot35^(@)-1)/(cot55^(@)+cot35^(@))

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  20. Express ((sqrt(3)cos 25^(@)+sin25^(@)))/(2) as a sine of an angle.

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