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If A = B = 45° , show that: sin (A - B) = sin A cos B - cos A sin B - Mathematics

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Sum

If A = B = 45° ,
show that:
sin (A - B) = sin A cos B - cos A sin B

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Solution

Given that A = B = 45°

LHS = sin (A – B)

= sin ( 45° – 45°)

= sin 0°

= 0

RHS = sin A cos B – cos A sin B

= sin 45° cos 45° – cos 45° sin 45°

= `(1)/(sqrt2) (1)/(sqrt2) – (1)/(sqrt2) (1)/(sqrt2)`

= 0

LHS = RHS

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 (B) | Q 3.1 | Page 293
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