Question

tanA÷1+secA+1+secA÷tana=​

Answer 1

Answer:

mark,as brainlist

Explanation:

complete ur question frst dear

Answer 2

$\;\;\underline{\textbf{\textsf{ Given:-}}}$

• $\sf \dfrac{tan\theta}{1+sec\theta}+\dfrac{1+sec\theta}{tan\theta}$

$\;\;\underline{\textbf{\textsf{ To Find:-}}}$

• Value of $\sf \dfrac{tan\theta}{1+sec\theta}+\dfrac{1+sec\theta}{tan\theta}$

$\;\;\underline{\textbf{\textsf{Solution :-}}}$

$\underline{\:\textsf{Given that :}}$

• $\sf \dfrac{tan\theta}{1+sec\theta}+\dfrac{1+sec\theta}{tan\theta}$

$\underline{\:\textsf{Then :}}$

$\dashrightarrow \sf \dfrac{tan^2\theta+(1+sec\theta)^2}{tan\theta(1+sec\theta)}\\\\ \dashrightarrow \sf \dfrac{(tan^2\theta+1)+sec^2\theta+2sec\theta}{tan\theta(1+sec\theta)}\\\\ \dashrightarrow \sf \dfrac{sec^2\theta+sec^2\theta+2sec\theta}{tan\theta(1+sec\theta)}\\\\\dashrightarrow \sf \dfrac{2sec^2\theta+2sec\theta}{tan\theta(1+sec\theta)}\\\\ \dashrightarrow \sf \dfrac{2sec\theta(sec\theta+1)}{tan\theta(sec\theta+1)}\\\\\\\dashrightarrow \sf \dfrac{2}{sin\theta}\\\\\dashrightarrow \sf 2cosec \theta$

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ㅤ$\;\;\underline{\textbf{\textsf{ Need to know :-}}}$

$\ \; \sf sec^2\theta-tan^2\theta=1\\\\ \sf sec^2\theta=1+tan^2\theta\\\\\sf \ \; tan\theta=\dfrac{sin\theta}{cos\theta}\\\\\sf \ \; sec\theta=\dfrac{1}{cos\theta}$

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