Question 792275
prove that 15tan^2(x) +4sec^2(x) = 23
solve for x:
{{{15 tan^2(x)+4sec^2(x)=23}}}
{{{15 (sin^2(x)/cos^2(x))+(4/cos^2(x))=23}}}
{{{(15 sin^2(x)+4)/(cos^2(x))=23}}}
{{{15 sin^2(x)+4=23 cos^2(x)}}}
{{{15 sin^2(x)+4=23(1-sin^2(x))}}}
{{{15 sin^2(x)+4=23-23sin^2(x)}}}
{{{38 sin^2(x)=19}}}
sin^2(x)=19/38=1/2
sin(x)=√1/√2
x=π/4
Check:
15tan^2(x)=15tan^2(π/4)15*1=15
4sec^2(x)=4/cos^2(π/4)=4/(1/2)=8
15tan^2(x)+15tan^2(x)=15+8=23
Given identity is true if x=π/4