Question

Explain the steps plzz

Answer 1

this is the solution of 4(ii)......

Answer 2

(i)

LHS = cos(A+B) cos(A-B) ------ (*)

We know that cos(A + B) = cosA cosB - sin A sin B  ----- (1)

We know that cos(A - B) = cos A cos B + sin A sin B  ----- (2)

Substitute (1) & (2) in (*), we get

(cos A cosB - sinA sinB)(cosA cosB + sinA sinB)

We know that (a-b)(a + b) = a^2 - b^2

Where a = cosAcosB, b = sinAsinB

cos^2Acos^2B - sin^2Asin^2B

(1 - sin^2A)cos^2B - sin^2A(1-cos^2B)

cos^2B - cos^2Bsin^2A - sin^2A + sin^2Acos^2B

cos^2B - sin^2A


LHS = RHS.




(ii)  LHS = sin(A + B)sin(A-B)  -------- (*)


We know that sin(A + B) = sinAcosB + cosAsinB  ----- (1)

We know that sin(A-B) = sinAcosB - cosASinB  ------ (2)

Substitute (1) & (2) in (*), we get

(sinA cosB + cosA sinB)(sinAcosB - cosAsinB)

We know that (a + b)(a - b) = a^2 - b^2

Where a = sinAcosB, b = cosAsinB

sin^2A cos^2B - cos^2Asin^2B

(1-cos^2A)cos^2B - cos^2A(1 - cos^2B)

cos^2B - cos^2Acos^2B - cos^2A + cos^2Acos^2B

cos^2B - cos^2A


LHS = RHS.




<!Hope this helps!>