Math, asked by DilipJha14, 7 months ago

(1 + tan’0) (1 + coto)
1
(sin?0-sinºo)​

Answers

Answered by poojaramakrishnan83
1

Answer:

what is the question I can't understand??

Answered by SubhanjanDatta
0

Step-by-step explanation:

Answer:

Hence Proved

Step-by-step explanation:

Sin0(1+tan0)+cos0(1+cot0)=sec0+cosec0 prove this

\begin{gathered}Sin\theta(1+Tan\theta) + Cos\theta(1+Cot\theta)\\\\Tan\theta = \frac{Sin\theta}{Cos\theta} \: \& \:Cot\theta = \frac{Cos\theta}{Sin\theta}\\\\\implies Sin\theta(1+\frac{Sin\theta}{Cos\theta}) + Cos\theta(1+\frac{Cos\theta}{Sin\theta})\\\\\implies Sin\theta(\frac{Cos\theta + Sin\theta}{Cos\theta}) + Cos\theta(\frac{Sin\theta + Cos\theta}{Sin\theta})\\\\\end{gathered}

Sinθ(1+Tanθ)+Cosθ(1+Cotθ)

Tanθ=

Cosθ

Sinθ

&Cotθ=

Sinθ

Cosθ

⟹Sinθ(1+

Cosθ

Sinθ

)+Cosθ(1+

Sinθ

Cosθ

)

⟹Sinθ(

Cosθ

Cosθ+Sinθ

)+Cosθ(

Sinθ

Sinθ+Cosθ

)

\begin{gathered}\implies (Cos\theta + Sin\theta)(\frac{Sin\theta}{Cos\theta} + \frac{Cos\theta}{Sin\theta})\\\\\implies (Cos\theta + Sin\theta)(\frac{Sin^2\theta + Cos^2\theta}{Cos\theta Sin\theta})\\\\Sin^2\theta + Cos^2\theta = 1\\\\\implies (Cos\theta + Sin\theta)(\frac{1}{Cos\theta Sin\theta})\\\end{gathered}

⟹(Cosθ+Sinθ)(

Cosθ

Sinθ

+

Sinθ

Cosθ

)

⟹(Cosθ+Sinθ)(

CosθSinθ

Sin

2

θ+Cos

2

θ

)

Sin

2

θ+Cos

2

θ=1

⟹(Cosθ+Sinθ)(

CosθSinθ

1

)

\begin{gathered}\implies \frac{Cos\theta}{Cos\theta Sin\theta} + \frac{Sin\theta}{Cos\theta Sin\theta}\\\\\implies \frac{1}{Sin\theta} + \frac{1}{Cos\theta}\\\\\implies Cosec\theta + Sec\theta\\\\= RHS\end{gathered}

CosθSinθ

Cosθ

+

CosθSinθ

Sinθ

Sinθ

1

+

Cosθ

1

⟹Cosecθ+Secθ

=RHS

( PROVED )

.

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