Question

sin square 15 degree+sin square25 degree+ sin square65 degree + sin square 75 degree=

Answer 1

Question:

sin²15°+sin²25°+ sin²65° + sin ²75° =

Answer:

Heya mate !!!

Here is ur answer!!

= sin²15°+sin²25°+ sin²65° + sin ²75°

= sin²15° + sin²25° + cos²(90-65) + cos ²(90-75)

= sin²15°+ sin²25° + cos²25°+ cos²15°

= (sin²15°+ cos²15°) + (sin²25°+ cos²25°)

By trigonometric Identity,

[sin ² A+ cos² A = 1]

= 1+1

=2

•°• sin²15°+sin²25°+ sin²65° + sin ²75° = 2

Answer 2

Step-by-step explanation:

sin²15 + sin²25 + sin²65 + sin²75

= sin²15 + sin²75 + sin²25 + sin²65

since, sin²A = cos² ( 90 - A ),

sin²15 + cos² ( 90-15 ) + sin²25 + cos² ( 90-65 )

= sin²15 + cos²15 + sin²25 + cos²25

we know that, sin²A + cos²A = 1

therefore,

= ( sin²15 + cos²15 ) + ( sin²25 + cos²25 )

= 1 + 1

= 2