Question

if tan theta + sec theta = M then prove that sec theta = m square + 1 upon 2 m

Answer 1

Answer is attached.

Hope this helps you...:)

Answer 2

Answer:

$If\:tan\theta+sec\theta= m \: then \\sec\theta = \frac{m^{2}+1}{2m}$

Step-by-step explanation:

$tan\theta+sec\theta= m \:--(1)$

$We\:know \:the \\ trigonometric\: identity \\sec^{2}\theta-tan^{2}\theta=1$

$\implies (sec\theta+tan\theta)(sec\theta-tan\theta)=1$

$\implies m(sec\theta-tan\theta)=1$

$\implies sec\theta-tan\theta=\frac{1}{m}\:---(2)$

/* Add equations (1) and (2) ,we get

$\implies 2sec\theta = m+\frac{1}{m}$

$\implies 2sec\theta = \frac{m^{2}+1}{m}$

$\implies sec\theta = \frac{m^{2}+1}{2m}$

Therefore,

$If\:tan\theta+sec\theta= m \: then \\sec\theta = \frac{m^{2}+1}{2m}$

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