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If sin x = cos x and x is acute, state the value of x - Mathematics

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Sum

If sin x = cos x and x is acute, state the value of x

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Solution

The angle, x is acute and hence we have, 0 < x
We know that
cos2x + sin2 x = 1
⇒ 2sin2 x = 1

⇒ sin x = `(1)/(sqrt2)`

⇒ x = 45°

Concept: Trigonometric Ratios of Some Special Angles
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APPEARS IN

Selina Concise Mathematics Class 9 ICSE
Chapter 23 Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Exercise 23 (A) | Q 7.1 | Page 291
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