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# Given A = 60° and B = 30°, prove that : tan (A - B) = tan A – tan B 1 + tan A . tan B - Mathematics

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Sum

Given A = 60° and B = 30°,
prove that : tan (A - B) = (tan"A" – tan"B")/(1 + tan"A".tan"B")

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#### Solution

LHS = tan(A – B)

= tan (60° – 30°)

= tan30°

= (1)/(sqrt3)

RHS = (tan"A" –  tan"B")/(1 + tan 60°. tan 30°)

= (tan60° – tan30°)/(1+tan 60°.tan30°)

= (sqrt3 – 1/(sqrt3))/(1 + sqrt3(1/sqrt3))

= (2)/(2sqrt3)

= (1)/sqrt3

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 1.4 | Page 293
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