Help solve please

Question

Which of the following is equivalent to 5cos^2 (theta) - 6sec^2 (theta) + 5sin^2 (theta) + 6tan^2 (theta) 11 6sec^2 (theta); 5tan(theta) None of the above

Answer 1

5cos²(θ)-6sec²(θ)+5sin²(θ)+6tan²(θ)

Use cos²(θ)+sin²(θ)=1 and tan²(θ)+1 = sec²(θ)

5 -6(tan²(θ) +1)+6tan²(θ)

5 -6tan²(θ) +6+6tan²(θ)

5+6 = 11 Since 6tan²(θ) cancel each other