Question

If θ is an acute angle of a right angled triangle, then which of the following equation is not true?

(A) sinθ cotθ = cosθ

(B) cosθ tanθ = sinθ

(C) cosec²θ − cot²θ = 1

(D) tan²θ − sec²θ = 1

Answer 1

Correct option is (D) tan²θ − sec²θ = 1

(A) sinθ cotθ = cosθ

\(\frac 1{\sqrt 2} \times 1 = \frac 1{\sqrt 2}\)

\(\frac 1{\sqrt 2} = \frac 1{\sqrt 2}\)

(B) cosθ tanθ = sinθ

\(\frac 1{\sqrt 2} \times 1 = \frac 1{\sqrt 2}\)

\(\frac 1{\sqrt 2} = \frac 1{\sqrt 2}\)

(C) cosec²θ − cot²θ = 1

\((\sqrt{2})^2 - 1^2 = 1\)

\(2 - 1 = 1\)

\(1 = 1\)

(D) tan²θ − sec²θ = 1

\(1 - (\sqrt 2)^2 = 1\)

\(1 - 2 = 1\)

\(-1 = 1\)