Question

prove that
Sin (45+theta ) - Sin (45-theta = root 2sintheta ​

Answer 1

Step-by-step explanation:

Form a general relation for sin(A + B) - sin(A - B):

=> {sinA.cosB + cosA.sinB} - {sinA.cosB - cosA.sinB}

=> sinA.cosB + cosA.sinB - sinA.cosB + cosA.sinB}

=> 2cosA.sinB

In the question, A = 45° & B = theta

So,

sin(45° + theta) - sin(45° - theta) is:

=> 2cos45°.sin(theta)

=> 2(1/√2).sin(theta)

=> √2 sin(theta) proved