Question

(tan x +1)/ tan x= sec^2 x

Answer 1

Answer:

$\huge{\fbox{\fbox{\bigstar{\mathfrak{\red{Answer}}}}}}$

Starting from:⤵️⤵️

$</p><p></p><p>{cos}^{2} (x)+ {sin}^{2} (x)=1</p><p></p><p>$

Divide both sides by cos²(x) to get:

cos²(x) ÷ cos²(x) + sin²(x) ÷ cos²(x)=1 ÷ cos²(x)

which simplifies to:

1+tan²(x)=sec²(x)

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Answer 2

||✪✪ CORRECT QUESTION ✪✪||

Prove That :- (tan²x +1)= sec^2x ?

|| ✰✰ ANSWER ✰✰ ||

we know That, sin²x + cos²x = 1

→ sin²x + cos²x = 1

Dividing both sides by cos²x we get,

→ (sin²x/cos²x) + (cos²x/cos²x) = (1/cos²x)

Now, putting (sinx/cosx) = tanx in LHS, and (1/cosx) = secx in RHS,

→ (Tan²x) + 1 = sec²x (Hence, Proved).

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$\begin{lgathered}\begin{cases} \Longrightarrow \sf \: \sin^{2}\theta+\cos^{2}\theta=1\\ \bf\Longrightarrow \sec^{2}\theta-\tan^{2}\theta=1\\ \bf\Longrightarrow \cosec^{2}\theta-\cot^{2}\theta=1\\ \end{cases}\end{lgathered}$