Question

the value of sec8teta-1/sec4teta-1

Answer 1

Answer:  4cos²2θcos4θ/cos8θ    Step-by-step explanation: (sec8θ-1)/(sec4θ-1) =(1/cos8θ-1)/(1/cos4θ-1) =[(1-cos8θ)/cos8θ]/[(1-cos4θ)/cos4θ] =(2sin²4θ/cos8θ)/(2sin²2θ/cos4θ)      [∵, 1-cos2θ=2sin²θ] =2(2sin2θcos2θ)²/cos8θ×cos4θ/2sin²2θ =4cos²2θcos4θ/cos8θ RHS tan8θ/tan2θ =(sin8θ/cos8θ)/(sin2θ/cos2θ) =2sin4θcos4θ/cos8θ×cos2θ/sin2θ =2.2sin2θcos2θcos4θ/cos8θ×cos2θ/sin2θ =4cos²2θcos4θ/cos8θ