Question

if tan2x=3/4 then 4cos4x+3sin4x=

Answer 1

We have to find the value of 4cos4x + 3sin4x if tan2x = 3/4.

here, tan2x = 3/4 = p/b

we know, h² = p² + b²  [ from Pythagorus theorem ]

= 3² + 4² = 5²

⇒ h = 5

so, sin2x = p/h = 3/5

and cos2x = b/h = 4/5

we know,

• sin2Ф = 2sinФcosФ
• cos2Ф = cos²Ф - sin²Ф

∴ sin4x = 2sin2x cos2x = 2 × 3/5 × 4/5 = 24/25

cos4x = cos²2x - sin²2x = (4/5)² - (3/5)² = 7/25

now, 4cos4x + 3sin4x

= 4(7/25) + 3(24/25)

= 28/25 + 72/25

= 100/25

= 4

Therefore the value of 4cos4x + 3sin4x is 4.