Question

If sec theta + tan theta = p, then find value of cosec theta

Answer 1

step by step explanation✌✌✌✌✌

Answer 2

$\sec(x) + \tan(x) = p \\ \sec(x) + ( \sec(x) \div \csc(x)= p \\ \sec(x) (1 + (1 \div \csc(x)) = p \\ p \div \sec(x) = 1 + (1 \div \csc(x) ) \\ (\sec(x) + \tan(x)) \div \sec(x) = 1 + (1 \div \csc(x))$

LHS :-

$(\sec(x) + \tan(x)) \div \sec(x) \\ 1 + ( \tan(x) \div \sec(x)) \\ = 1 + (\ \csc(x) \div { \sec( x ) }^{2} )$

LHS = RHS

$\csc(x) \div { \sec(x) }^{2} = 1 \div \csc(x) \\ { \csc(x) }^{2} \div { \sec(x) }^{2} = 1 \\ { \csc(x) }^{2} = { \sec(x) }^{2} \\ \csc(x) = \sec(x)$

OR

$\csc(x) = p \: - \tan(x)$

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