CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

\frac{1}{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

none of these

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D none of these
Given,

$A, B$ are complementary angles.

$\Rightarrow A = 90 - B$

Now,

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

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

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

$= 1$

Suggest Corrections

thumbs-up

0

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

then prove that

Δ

must be isosceles.

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)

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Trigonometric Ratios of Specific Angles

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Standard Values of Trigonometric Ratios

Standard X Mathematics

Join BYJU'S Learning Program

CrossIcon