1. If \(sinθ−cosθ=0,\) \( (0°<θ<90°)\) and \(secθ+cosecθ=x\), then the value of \(x\) is—?

(a) \(1\) (b) \(2\) (c) \(\sqrt2\) (d) \(2\sqrt2\)

2. If \(\frac{\sinθ + \cosθ}{\sinθ - \cosθ} = 7\), then what is the value of \(\tanθ\)?

3. If \( \tan θ + \cot θ = 2 \), then what is the value of \( \tan^7 θ + \cot^7 θ \)?

4. If \(3\sinθ + 4\cosθ = 5\), then what is the value of \(4\sinθ - 3\cosθ\)?

5. If \( \secθ + \tanθ = x \), then \( \tanθ \) = ?

(a) \(\cfrac{x^2+1}{x}\) (b) \(\cfrac{x^2-1}{x}\) (c) \(\cfrac{x^2+1}{2x}\) (d) \(\cfrac{x^2-1}{2x}\)

6. If \( x = a \cosθ \) and \( y = b \sinθ \), then \( b^2 x^2 + a^2 y^2 \) = ?

(a) \(a^2b^2\) (b) \(ab\) (c) \(a^4b^4\) (d) \(a^2+b^2\)

7. If \( a \cosθ + b \sinθ = 4 \) and
\( a \sinθ - b \cosθ = 3 \), then \( a^2 + b^2 \) = ?

(a) 7 (b) 12 (c) 25 (d) 32

8. If \( \cotθ = \cfrac{15}{8} \), then find the value of
\(\cfrac{(2+2\sinθ)(1-\sinθ)}{(1+\cosθ)(2-2\cosθ)}\).

(a) \(0\) (b) \(225\) (c) \(64\) (d) \(\cfrac{225}{64}\)

9. If \( \sinθ + \cosθ = \sqrt2 \sin(90° – θ) \), then find the value of \( \cotθ \).

(a) \(\cfrac{\sqrt2}{3}\) (b) \(1\) (c) \(\sqrt2\) (d) \(\sqrt2+1\)

10. If \(\sin θ \cos θ = \frac{1}{2}\), then calculate the value of \((\sin θ + \cos θ)\).