Question

If tan x =b/a prove that acos 2x + bsin 2x = a
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Answer 1

$\huge\bf{Answer:-}$

Refer the attachment.

Answer 2

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Tan x = b/a

$\LARGE\underline{\underline{\sf \red{T}\blue{o}\:\green{F}\orange{i}\pink{n}\red{d}:}}$

Prove :---- acos 2x + bsin 2x = a

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Formula to be used :------

• Tan A = Sin A / cosA
• cos(A-B) = cosACosB + sinAsinB
• cos(-x) = cosx

See my solution in Easiest way now ,:---------

it is given that Tan x = b/a

and we know that tan x = sinx/cosx

so,

sinx/cosx = b/a

comparing we get,

b = sinx

a = cosx

Putting This value in Question now we get,

acos 2x + bsin 2x

(cosx)(cos2x) + sinx(sin2x)

= cosAcosB + sinAsinB

= Cos(x - 2x)

= Cos(-x)

= Cosx = a $\huge\underline\purple{\mathcal PROVED}$

$\color {red}\large\bold\star\underline\mathcal{Extra\:Brainly\:Knowledge:-}$

$\underline\textsf{Double Angle Identities}$

→ sin²θ = 2sinθcosθ

= $\frac{2 \tanθ}{1+ \tan^{2}θ}$

→ cos2θ = cos²θ- sin²θ

= 1 - 2sin²θ

= 2cos²θ- 1

= $\frac{1- \tan^{2}θ}{1+ \tan^{2}θ}$

→Tan2θ = $\frac{2 \tanθ}{1- \tan^{2}θ}$

$\mathcal{BE\:\:BRAINLY}$