Question

tanx=sin45 multiply by cos 45 added with sin 30. find the value of x

Answer 1

tan x = sin 45° X cos 45° + sin 30°
tan x = 1/√2 X 1/√2 + 1/2
tan x = 1/2 + 1/2
tan x = 1                                     → A

But,
tan 45° = 1                                  → B

From A & B, R.H.S. is equal,
∴ tan x = tan 45°
⇒      x = 45°

Answer 2

Answer:

The value of ${x}=45^{\circ}$

Step-by-step explanation:

Trigonometric Identities are useful whenever trigonometric functions exist concerned in a presentation or an equation. Trigonometric Identities stand true for every value of variables happening on both sides of an equation. Geometrically, these identities involve specific trigonometric functions (such as sine, cosine, tangent) of one or more angles.

The reciprocal trigonometric identities are:

• Sin θ = 1/Csc θ or Csc θ = 1/Sin θ
• Cos θ = 1/Sec θ or Sec θ = 1/Cos θ
• Tan θ = 1/Cot θ or Cot θ = 1/Tan θ

Given,

$\tan x=\sin 45^{\circ} *\cos 45^{\circ}+\sin 30^{\circ}$

To find,

The value of x

$&\tan x=\left(\frac{1}{\sqrt{2}} \times \frac{1}{\sqrt{2}}\right)+\frac{1}{2} \\\quad\left[\because \sin 30^{\circ}=\frac{1}{2}, \cos 45^{\circ}=\sin 45^{\circ}=\frac{1}{\sqrt{2}}\right]$

$&\tan x=\left(\frac{1}{\sqrt{2}}\right)^{2}+\frac{1}{2}$

Simplifying the equation,

$&\tan x=\frac{1}{2}+\frac{1}{2}$

$&\tan x=\frac{2}{2}$

By dividing the terms We get,

$&\tan \mathrm{x}=1$

$&\tan 45^{\circ}=1$

Hence,

$&\tan x=\tan 45^{\circ}$

Therefore,

${x}=45^{\circ}$

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