If x = sin θ + cos θ and y = sin θ – cos θ, then the value of (x2 + y2 - 1) × (x2 + y2 + 5) will be
1). 6
2). 9
3). 7
4). 10
Given, x = sin θ + cos θ and y = sin θ – cos θ
Thus, x + y = 2sinθ
Also, xy = sin2θ – cos2θ
(x + y)2 = x2 + y2 + 2xy
⇒ 4sin2θ = x2 + y2 + 2sin2θ – 2cos2θ
⇒ x2 + y2 = 2(sin2θ + cos2θ) = 2
Thus, (x2 + y2 – 1) × (x2 + y2 + 5) = (2 – 1) × (2 + 5) = 71. What is the value of sin( – π/3) + cos( – π/6)?
6. If cos 45° - sec 60° = x, then the value of x is
7. If $Cos\theta $ = $\frac{5}{13}$, then $Cosec\theta $ = ?
8. What is the value of sin $\frac{-7π}{4}$?
9. The value of $cosec^{2}18^{0} - \frac{1}{cot^{2}72^{0}}$ is
10. sec2θ + tan2θ \( = \frac{5}{3}\) and 0 ≤ θ ≤ \(\frac{{\rm{\pi }}}{2}\) then the value of θ -