Find the Value of X in the Following : Tan 3x = Sin 45º Cos 45º + Sin 30º - Mathematics

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Sum

Find the value of x in the following :

tan 3x = sin 45º cos 45º + sin 30º

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Solution 1

tan 3x = sin 45º cos 45º + sin 30º

`\Rightarrow tan3x=\frac{1}{\sqrt{2}}\times\frac{1}{\sqrt{2}}+\frac{1}{2}`

`\Rightarrow tan3x=\frac{1}{2}+\frac{1}{2} `

⇒ tan 3x = 1

⇒ tan 3x = tan 45º

⇒ 3x = 45º ⇒ x = 15º

Solution 2

`tan x= 1/sqrt2 . 1.sqrt2 + 1/2`    `[∵ sin 45^@ = 1/sqrt2   cos 45^@ = 1/sqrt2  sin 30^@ = 1/2]`

`tan x = 1/2 + 1/2`

tan x = 1

`tan x = tan 45^@`

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Chapter 10: Trigonometric Ratios - Exercise 10.2 [Page 42]

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RD Sharma Class 10 Maths
Chapter 10 Trigonometric Ratios
Exercise 10.2 | Q 23 | Page 42

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