Question

Sin ²1⁰ + Sin ²2⁰ + Sin ²3⁰+ Sin ²87⁰ + Sin ²88⁰+Sin²89⁰= ​

Answer 1

Answer:

3

Step-by-step explanation:

sin(90-a) = cosa

and sin^2a+cos^2a= 1

by using this

(sin^2(1)+sin^2(89))+((sin^2(2)+sin^2(88))+(sin^2(3)+sin^2(87))

= (sin^2(1)+cos^2(1))+(sin^2(2)+cos^2(2))+(sin^2(3)+cos^2(3))

=1+1+1

=3

Answer 2

Answer:

3

Step-by-step explanation:

Given :

Sin ²1⁰ + Sin ²2⁰ + Sin ²3⁰+ Sin ²87⁰ + Sin ²88⁰ + Sin²89⁰

To find :

The value of the given expression

Solution :

We know that,

$\boxed{\sin x = \cos (90-x)}$

So,

$\longmapsto \sin89^{\circ} = \cos(90-89)^{\circ} = \cos1^{\circ}$

$\longmapsto \sin88^{\circ} = \cos(90-88)^{\circ} = \cos2^{\circ}$

$\longmapsto \sin87^{\circ} = \cos(90-87)^{\circ} = \cos3^{\circ}$

Now, rewriting the question with the values, we get,

$\implies \sin^21^{\circ} + \sin^22^{\circ} + \sin^23^{\circ} + \cos^23^{\circ} +\cos^22^{\circ} + \cos^21^{\circ}$

We know that,

$\boxed {\mathrm {\sin^2 x+ \cos^2x = 1}}$

So, rearranging the terms, we get,

$\implies \underline {\sin^21^{\circ} + \cos^21^{\circ}} + \underline {\sin^22^{\circ} +\cos^22^{\circ} } +\underline {\sin^23^{\circ} + \cos^23^{\circ} }$

$\implies 1 + 1 + 1$

$\implies \huge{\texttt{\underline {\underline{3}}}}$

Hope it helps!!