Question

Show that cot theta + tan theta = Sec theta Cosec theta​

Answer 1

$\bf\huge\textbf {\underline {\underline {Solution :-}}} \\ \\ \\ \bf\huge { LHS = Cot\theta + Tan\theta}\\ \\ \\ \bf\huge{\to {\dfrac {Cos\theta}{Sin\theta}}} + \dfrac {Sin\theta}{Cos\theta}\\ \\ \\ \bf\huge{\to {\dfrac {Cos^2 \theta + Sin^2 \theta}{Sin\theta \: Cos\theta}}}\\ \\ \\ \bf\huge {\to {\dfrac {1}{Sin\theta \: Cos\theta}}} \\ \\ \\ \bf\huge {\to {Cosec\theta \: Sec\theta = RHS}}$

Answer 2

Heya!

Here is ur answer.....

To show :

cotΦ +tanΦ = secΦ • cosecΦ

LHS :

= cotΦ + tanΦ

= cosΦ/sinΦ + sinΦ/cosΦ

= cos²Φ+sin²Φ/(sinΦ)(cosΦ)

= 1/(sinΦ)(cosΦ)

= 1/sinΦ × 1/cosΦ

= cosecΦ × secΦ

= secΦ × cosecΦ

RHS :

= secΦ × cosecΦ

Therefore,

cotΦ +tanΦ = secΦ × cosecΦ

Here, LHS = RHS

Hence proved!