Question

If tan A = 1 and tan B = 3, find the value of the following, cos A cos B - sin A sin B

Answer 1

tan x = opposite side / adjacent

side

tan x = opposite side / adjacent

side

cos x = adjacent side /

Hypotenuse side

sin x = opposite side /

Hypotenuse side

According to Pythagorean theorem

(AB) ^2= (BC) ^2+ (CA) ^2

tan A = 1

opposite side = 1

adjacent side = 1

Hypotenuse = √2

cos A = 1/√

sin A = 1/√2

tan B = 3

opposite side = 3

adjacent side = 1

Hypotenuse = √10

cos B = 1/√10

sin B = 3/√10

cos A cos B - sin A sin B

= (1/√2) (1/√10) - (1/√2) (3/√10)

= (1/√20) - (3/√20)

= -2/2√5

= -1/√5

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