CBSE Class 11-science Answered

Use the following formulae,

sin(A+B) = sinAcosB + cosAsinB

sin45 = sin30cos15 + cos30sin15

1/2^1/2 = (cos15)/2 + (3^1/2sin15)/2.............(1)

cos45 = cos30cos15 - sin30sin15

1/2^1/2 = (3^1/2cos15)/2 - (sin15)/2...............(2)

Solving (1) and (2) for cos 15 gives,

cos 15 = (1 + 3)/2,

Similarly we can find sin15,

with the found values of sin15 and cos 15, we can write

sin 15 = 3sin5 - 4sin³5

Solving this equation gives sin 5,

sin 10 can be similarly obtained by using the formula, sin 10 = 2sin5cos5.

Others can be derived from sin and cos values.

Regards,

Team,

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