Question

(1+cot2theta)tantheta/sec2theta=cot2theta
​

Answer 1

Proof :

L.H.S. =

$\frac{(1+cot^{2}\theta)\times tan\theta}{sec^{2}\theta} </p><p>sec </p><p>2</p><p> θ</p><p>(1+cot </p><p>2</p><p> θ)×tanθ$

$=\frac{cosec^{2}\theta \times tan\theta}{sec^{2}\theta}= </p><p>sec </p><p>2</p><p> θ</p><p>cosec </p><p>2</p><p> θ×tanθ$

$since cosec^{2}\theta-cot^{2}\theta=1cosec </p><p>2</p><p> θ−cot </p><p>2</p><p> θ=1$

$=\frac{\frac{1}{sin^{2}\theta}\times \frac{sin\theta}{cos\theta}}{\frac{1}{cos^{2}\theta}}= </p><p>cos </p><p>2</p><p> θ</p><p>1</p><p>$

$sin </p><p>2</p><p> θ</p><p>1</p><p> </p><p> × </p><p>cosθ</p><p>sinθ</p><p>$

$=\frac{sin\theta\times cos^{2}\theta}{sin^{2}\theta\times cos\theta}= </p><p>sin </p><p>2</p><p> θ×cosθ</p><p>sinθ×cos </p><p>2</p><p> θ$

$=\frac{cos\theta}{sin\theta}= </p><p>sinθ</p><p>cosθ</p><p>$

$=cot\theta=cotθ = R.H.S.$

Hence, proved.

• Trigonometry : It is the study of angles and its sine, cosine, tangent, cosectant, sectant, cotangent ratios.

• Identity Rules :

>> sinθ * cosecθ = 1

>> cosθ * secθ = 1

>> tanθ * cotθ = 1

>> sin²θ + cos²θ = 1

>> sec²θ - tan²θ = 1

>> cosec²θ - cot²θ = 1