Question

sin^2(5)+sin^2(10)....sin^2(90)=?

Answer 1

HELLO DEAR,

we know that:-

cos theta = sin(90-theta)

---------or----------

cos²theta = sin²(90-theta)

-------------and------------

sin²theta+cos ²theta = 1


--------------------------------------------------

sin ²(5) +sin²(85) +sin²(10) +sin²(80) +sin²(15)+sin²(75) +.........+sin²(45) +......sin²(90)



=> sin²5° + sin²(90-5)° +sin²10°+sin²(90-10)°+sin²15°+sin²(90-15)°+......+(1/√2)²+.......+(1)²


=> (sin²5+cos ²5) +( sin²10+cos ²10) +
(sin²15+cos²15) +......1/2+....1

there are now 8terms equal to 1

=> 1+1+1....1/2+...1

=> 8+1/2+1

=> 9+1/2

=> (18+1)/2

=> 19/2

=> 9.5


I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

Hi,

Please see the attached file!


Thanks