If \(\cos\theta+\sec\theta=8\), what is the value of \(\cos^2\theta+\sec^2\theta\)?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 62
\(\cos\theta\) and \(\sec\theta\) are reciprocals, so their product is 1. Squaring the sum then gives the sum of squares plus twice this product.
\((\cos\theta+\sec\theta)^2=\cos^2\theta+\sec^2\theta+2\cos\theta\sec\theta\)
\(64=\cos^2\theta+\sec^2\theta+2\)
\(\cos^2\theta+\sec^2\theta=62\)