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Trigonometric Functions

Short Answer Type

571.

Prove that:

$sin open parentheses straight x over 2 close parentheses space equals space plus-or-minus square root of fraction numerator 1 minus cosx over denominator 2 end fraction end root$

103 Views

572.

Prove that:

$tan open parentheses straight x over 2 close parentheses equals plus-or-minus square root of fraction numerator 1 minus cosx over denominator 1 plus cosx end fraction end root.$

210 Views

573.

Prove that:

$2 space sinA space cosB space equals space sin left parenthesis straight A plus straight B right parenthesis space plus space sin left parenthesis straight A minus straight B right parenthesis$

101 Views

574.

Prove that:
2 cosA sinB = sin (A + B) - sin (A - B)

130 Views

575.

Prove that:
2 cosA cosB = cos (A + B) + cos (A - B)

113 Views

576.

Prove that:
-2 sinA sinB = cos (A + B) - cos (A - B)

218 Views

577.

Prove the following:

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91 Views

578.
Prove the following:

$sin space straight C space minus space sin space straight D space equals space 2 cos fraction numerator straight C plus straight D over denominator 2 end fraction sin fraction numerator straight C minus straight D over denominator 2 end fraction$

Let $fraction numerator straight C plus straight D over denominator 2 end fraction equals straight x space space and space fraction numerator straight C minus straight D over denominator 2 end fraction equals straight y$

R.H.S. = $2 cos open parentheses fraction numerator straight C plus straight D over denominator 2 end fraction close parentheses space sin open parentheses fraction numerator straight C minus straight D over denominator 2 end fraction close parentheses space equals space 2 space cosx space siny$

= sin (x + y) - sin (x - y)

= $sin open parentheses fraction numerator straight C plus straight D over denominator 2 end fraction plus fraction numerator straight C minus straight D over denominator 2 end fraction close parentheses minus sin open parentheses fraction numerator straight C plus straight D over denominator 2 end fraction minus fraction numerator straight C minus straight D over denominator 2 end fraction close parentheses$

= sin C - sin D = L.H.S.

Hence, $space space space space sin space straight C minus space sin space straight D space equals space 2 cos fraction numerator straight C plus straight D over denominator 2 end fraction sin fraction numerator straight C minus straight D over denominator 2 end fraction$

100 Views

579.

Prove the following:

$space space cosC space plus space cosD space equals space 2 cos fraction numerator straight C plus straight D over denominator 2 end fraction cos fraction numerator straight C minus straight D over denominator 2 end fraction$

116 Views

580.

Prove the following:

$cosC space minus space cosD space equals space minus 2 sin fraction numerator straight C plus straight D over denominator 2 end fraction sin fraction numerator straight C minus straight D over denominator 2 end fraction$

90 Views

Previous Year Papers

Test Series

Test Yourself

Short Answer Type

578. Prove the following:

578.
Prove the following:

$sin space straight C space minus space sin space straight D space equals space 2 cos fraction numerator straight C plus straight D over denominator 2 end fraction sin fraction numerator straight C minus straight D over denominator 2 end fraction$