Question

Tan A 1

Tan B = root 3
Cos A cos B - sin A sin B

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Answer 1

Answer:

Given ,

• tan A = 1
• tanB = √3

To find :

• cos A cos B - sin A sin B

We are given ,

★ tanA = 1

→ tanA = tan45⁰

→ A = 45⁰

And

tanB = √3

→ tanB = tan60⁰

→ B = 60⁰

So,

cos A cos B - sin A sin B

= cos 45⁰ . cos 60⁰ - sin45⁰ . sin 60⁰

=( 1/√2). (1/2) - (1/√2). (√3/2)

=( 1/2√2) - (√3/2√2)

= (√2-√6)/4

$\huge\bold{Answer — \: \: \: \frac{ \sqrt{2} - \sqrt{6}}{4 } }$