Question

2.4) Find the value of cos15°, using 30° and 45°.​

Answer 1

Answer:

Please note: I won't be typing °, as I am lazy but all the angles are in degrees.

cos 15 = cos 45 - 30

cos A - B = cosAcosB - sinAsinB

= cos45cos30 - sin45sin30

= (1/√2)(√3/2) - (1/√2)(1/2)

= (1/√2)[√3/2 - 1/2]

= 1/√2[(√3-1)/2]

= (√3-1)/(2√2)

On rationalizing, this becomes:

(√6-√2)/(4)

Answer 2

Answer :

Cos (45-30) = Cos 15

This is in the form

Cos (A-b) = cosA. Cos B +SinA. SinB

A=45

B=30

= cos 45. Cos 30+sin45.sin30

= 1/root 2. root 3 /2 +1/root 2. 1/2

= root 3 /2root2 +1/2 root 2

= root 3 +1 /2 root 2

Now, rationalise

= root 3 +1/2root2 x root 2/root 2

= root 6 +root 2/4