Verify the identity 1sinBeta1sinBeta1sec2Beta Expand the pro

Verify the identity: (1+sinBeta)(1-sinBeta)=1/sec^2Beta Expand the product, and use a pythagorean identity. (1+sinBeta)(1-sinBeta)=1-_______== Use a reciprocal identity =____

Solution

(1+sinBeta)(1-sinBeta)

=(1+sinBeta -sinBeta-sin²Beta)

=(1 -sin²Beta)..................... pythagorean identity is sin²Beta+cos²Beta =1

=(cos²Beta).........................reciprocal identity is cosBeta=(1_/secBeta)

=(1_/sec²Beta)