Question

if secy=x+1/4x, prove that secy +tany=2x or 1/2x​

Answer 1

Step-by-step explanation:

$\tan(y) = \sqrt{( { (\sec(y)) }^{2} - 1) } \\ = \sqrt{(x + 1 \div 4x)^{2} - 1} \\ = \sqrt{( {x}^{2} + 1 \div 16 {x}^{2} +(1 \div 2) -1) } \\ = \sqrt{( {x}^{2} + 1 \div 16 {x}^{2} - (1 \div 2)) } \\ = \sqrt{ {(x - 1 \div 4x)}^{2} } = (x - 1 \div 4x)$

Now,

LHS =

$\sec(y) + \tan(y) = x +( 1 \div 4x) + x - (1 \div 4x) = 2x$

ANS, 2x