Question

Use fundamental identities​ and/or the complementary angle theorem to find the exact value of the given expression. Do not use a calculator. sec234°−tan234°

Answer 1

1

Explanation:

Given the expression sec²34°−tan²34°, to get the exact value using the fundamental identities​ and/or the complementary angle theorem, we will apply the trigonometry identity

From sin²θ+cos²θ = 1

Divide both sides of the expression by cos²θ

sin²θ/cos²θ+cos²θ/cos²θ = 1/cos²θ

tan²θ+1 =sec²θ

Since sec²θ= tan²θ+1, hence sec²34°= tan²34°+1... 1

Substituting equation 1 into the expression given in question we will have;

sec²34°−tan²34°

= (tan²34°+1)-tan²34°

collect like terms

= tan²34°-tan²34°+1

= 1

Hence the exact value of the expression sec²34°−tan²34° is 1