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If A + B = 45°, show that (1 + tan A) (1 + tan B) = 2. |
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Answer» A + B = 45° tan (A + B) = tan 45° = 1 (i.e) (tan A + tan B)/(1 - tan A tan B) = 1 tan A + tan B = 1 - tan A tan B ... (1) Now LHS = (1 + tan A) (1 + tan B) = tan A + tan B + tan A tan B + 1 = (1 – tan A tan B) + (tan A tan B + 1) from (1) = 2 = RHS |
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