Math, asked by ramdhakal12, 4 months ago

2sin²(45⁰ - A) = 1 - sin2A​

Answers

Answered by sakeenabeegum0
0

Step-by-step explanation:

How do I prove that [math]cos^2 (45 + x) - sin^2 (45 + x) = 0[/math]?

Why is term insurance crucial if you are self-employed?

Let’s understand what’s Term Insurance. Term insurance is fundamentally a type of life insurance that provides coverage at predete

This is not an identity, which can be proved.

This is an equation, which is to be solved, ie, to get the value of unknown quantity X

Let 45 + X be β

So, Cos² β - Sin²β =0

=> (Cosβ + Sinβ) (Cosβ - Sinβ)=0

On Squaring,

=> ( Cos²β +Sin²β + 2Cosβ.Sinβ)(Cos²β + Sin²β - 2Cosβ.Sinβ) =0

=> (1+ 2Cosβ.Sinβ)(1- 2Cosβ.Sinβ) =0

=> 1 - 4 Cos²β.Sin²β=0

=> 1 - 4Cos²β(1- Cos²β) =0

=> 1 - 4(Cosβ)² + 4(Cosβ)^4 =0

=> (2Cos²β —1)² =0

Now on finding square root

=> +,- ( 2Cos²β —1) = 0

=> 2Cos²β -1 =0

=> Cos²β = 1/2

=> Cosβ = +,- 1/√2

ie, cos (45 + x ) = +,- 1/√2

=> 45 + x = 0, 225 deg

=> x = 0, 180

VERIFICATION:

So, LHS= Cos²(45°+x) - Sin²(45° +x)

= Cos²45° — Sin²45°

=( 1/√2) — (1/√2)

= 0 = RHS

Similar questions