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Standard Values of Trigonometric Ratios

If A and B ar...

Question

If A and B are complementary angles then ${sin}^{2} A + {sin}^{2} B =$

A

0

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B

\frac{1}{2}

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C

2

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D

none of these

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Solution

The correct option is D none of these
Given,

$A, B$ are complementary angles.

$\Rightarrow A = 90 - B$

Now,

${sin}^{2} A + {sin}^{2} B$

$= {sin}^{2} (90 - B) + {sin}^{2} B$

$= {cos}^{2} A + {sin}^{2} B$

$= 1$

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Similar questions

α

β

complementary angles then

{sin}^{2} (90^{o} - α) + {sin}^{2} (90^{o} - β) =

a, b, c

{sin}^{2} \frac{A}{2}, {sin}^{2} \frac{B}{2}, {sin}^{2} \frac{C}{2}

A, B

are supplementary angles the

{sin}^{2} A + {sin}^{2} B =

A

B

C

be the angles of a triangle and

∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 1 + sin A & 1 + sin B & 1 + sin C sin A + {sin}^{2} A & sin B + {sin}^{2} B & sin C + {sin}^{2} C \end{matrix} ∣ ∣ ∣ ∣ ∣ = 0

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Δ

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A + B + C = 180^{o}

then prove the following:
(i)

{sin}^{2} A + {sin}^{2} B - {sin}^{2} C = 2 sin A sin B cos C

{sin}^{2} A + {sin}^{2} B + {sin}^{2} C = 2 (1 + cos A cos B cos C)

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