Question

if sec teta = 5/4 then show that ( sin teta - 2cos teta) / (ten teta - cos teta ) = 12/7​

Answer 1

Step-by-step explanation:

given equation is \frac{cos x+ sin x}{cos x - sin x} -\frac{cos x - sin x}{cos x + sin x}

cosx−sinx

cosx+sinx

−

cosx+sinx

cosx−sinx

taking LCM we get \frac{(cos x + sin x)*(cos x + sin x) - (cos x - sinx )*(cos x - sin x)}{(cos x - sin x)*(cos +sin x)}

(cosx−sinx)∗(cos+sinx)

(cosx+sinx)∗(cosx+sinx)−(cosx−sinx)∗(cosx−sinx)

=\frac{(cos x + sin x)^{2} - (cos x - sin x)^{2}}{cos^{2}x - sin^{2}x}

cos

2

x−sin

2

x

(cosx+sinx)

2

−(cosx−sinx)

2

=\frac{cos ^{2}x+sin^{2}x+2cos x sin x- cos^{2}x-sin^{2} x +2 cos x sinx}{cos 2x}

cos2x

cos

2

x+sin

2

x+2cosxsinx−cos

2

x−sin

2

x+2cosxsinx

since cos²∅-sin²∅=cos2∅

= \frac{4 cos x sin x}{cos 2x}

cos2x

4cosxsinx

= \begin{lgathered}\frac{2 sin2x}{cos 2x}\\\end{lgathered}

cos2x

2sin2x

since 2sin∅cos∅ = sin 2∅

= 2 tan2x