Question

If a =11π÷4
find the numerical value of sin2 a - cos2 a + 2 tan a – sec2 a.​

Answer 1

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

$\large\rm{ \dfrac{1}{2} - \dfrac{1}{2} - 2 - 2}$

$\large\fbox{\rm{ = -4}}$