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

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Sum

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

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Solution

Given that A = B = 45°

LHS = cos (A +  B)

= cos ( 45° + 45°)

= cos 90°

= 0

RHS = cos A cos B – sin A sin B

= cos 45° cos 45° – sin 45° sin 45°

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

= 0

LHS = RHS

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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 3.2 | Page 293
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