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Maths-

General

Easy

Question

If $tan space open parentheses x plus pi over 4 close parentheses equals a$ then $sec squared space x$ =

$1 + a^{2}$
$\frac{4 a}{(a + 1)^{2}}$
$\frac{2 (a^{2} + 1)}{(a + 1)^{2}}$
${(\frac{a - 1}{a + 1})}^{2}$

hint Hint:

Use tangent additive formula to solve the equation.

The correct answer is: $fraction numerator 2 open parentheses a squared plus 1 close parentheses over denominator left parenthesis a plus 1 right parenthesis squared end fraction$

$tan space open parentheses x plus pi over 4 close parentheses equals a fraction numerator tan x plus tan begin display style straight pi over 4 end style over denominator 1 minus tan x tan begin display style straight pi over 4 end style end fraction equals a fraction numerator tan x plus 1 over denominator 1 minus tan x end fraction equals a U sin g space c o m p o n e n d minus d i v i d e n d comma fraction numerator 1 plus tan x plus 1 minus tan x over denominator 1 plus tan x minus open parentheses 1 minus tan x close parentheses end fraction equals fraction numerator a plus 1 over denominator a minus 1 end fraction fraction numerator 2 over denominator 2 tan x end fraction equals fraction numerator a plus 1 over denominator a minus 1 end fraction fraction numerator 1 over denominator tan x end fraction equals fraction numerator a plus 1 over denominator a minus 1 end fraction therefore tan x equals fraction numerator a minus 1 over denominator a plus 1 end fraction N o w comma s e c squared x equals 1 plus tan squared x equals 1 plus open parentheses fraction numerator a minus 1 over denominator a plus 1 end fraction close parentheses squared equals fraction numerator open parentheses a plus 1 close parentheses squared plus open parentheses a minus 1 close parentheses squared over denominator open parentheses a plus 1 close parentheses squared end fraction therefore s e c squared x equals fraction numerator 2 open parentheses a squared plus 1 close parentheses over denominator open parentheses a plus 1 close parentheses squared end fraction$

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