Answer:
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