If a =11π÷4find the numerical value of sin2 a - cos2 a + 2 tan a –

1.	If a =11π÷4find the numerical value of sin2 a - cos2 a + 2 tan a – sec2 a.
Answer» QUESTION:- if θ = $\large\rm \dfrac{11\pi}{4}$ , then FIND the NUMERICAL VALUE of $\large\rm{ \sin^2 \theta - \cos^2\theta + 2 \ \tan\theta - \sec^2 \theta}$ Answer: $\large\rm{ \theta = \dfrac{11\pi}{4} = \Bigg ( 3 \pi - \dfrac{\pi}{4} \Bigg ) }$ ❥evaluation for sinθ $\large\rm{ \sin\theta = \sin \Bigg ( 3 \pi - \dfrac{\pi}{4} \Bigg ) }$ $\large\rm = \sin \dfrac{\pi}{4}$ $\large\rm = \sin 45^{\circ}$ $\large\rm = \dfrac{1}{\sqrt{2}}$ now sinθ $\large\rm = \dfrac{1}{\sqrt{2}}$ $\large\rm{ \therefore \sin^2 \theta = \dfrac{1}{2} }$ ❥evaluation for cosθ $\large\rm{ \cos\theta = \cos \Bigg ( 3 \pi - \dfrac{\pi}{4} \Bigg ) }$ $\large\rm{ = - \cos \dfrac{\pi}{4} }$ $\large\rm{ = - \cos 45^{\circ}}$ $\large\rm{ \cos\theta = - \dfrac{1}{\sqrt{2}}}$ $\large\rm{ \therefore \cos^2 \theta = \dfrac{1}{2} }$ ❥evaluation for tanθ $\large\rm{ \tan\theta = \tan \Bigg ( 3 \pi - \dfrac{\pi}{4} \Bigg ) }$ $\large\rm{ = - \tan \dfrac{\pi}{4} }$ $\large\rm{ = - \tan 45^{\circ}}$ $\large\rm{ \tan\theta = - 1}$ $\large\rm{ \therefore 2 \tan\theta = -2}$ now REQUIRED numerical value $\large\rm{ \dfrac{1}{2} - \dfrac{1}{2} - 2 - 2}$ $\large\fbox{\rm{ = -4}}$