Question

Sec square theta+tan theta=13 then tan theta=

Answer 1

SOLUTION

GIVEN

$\sf{} { \sec}^{2} \theta + \tan \theta = 13$

TO DETERMINE

$\sf{} \tan \theta$

EVALUATION

$\sf{} { \sec}^{2} \theta + \tan \theta = 13$

$\implies \sf{}1 + { \tan}^{2} \theta + \tan \theta = 13$

$\implies \sf{} { \tan}^{2} \theta + \tan \theta - 12 = 0$

$\implies \sf{} { \tan}^{2} \theta + (4 - 3)\tan \theta - 12 = 0$

$\implies \sf{} { \tan}^{2} \theta + 4\tan \theta - 3\tan \theta - 12 = 0$

$\implies \sf{}\tan \theta (\tan \theta + 4) - 3(\tan \theta + 4) = 0$

$\implies \sf{} (\tan \theta + 4) (\tan \theta - 3) = 0$

$\sf{} either \sf{} (\tan \theta + 4) = 0 \: or \: (\tan \theta - 3) = 0$

Now

$\sf{} (\tan \theta + 4) = 0 \: \:gives\: \: \tan \theta = - 4$

Again

$\sf{} (\tan \theta - 3) = 0 \: \:gives\: \: \tan \theta = 3$

FINAL ANSWER

$\sf{} \: \tan \theta = - 4 \: , \: 3$

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LEARN MORE FROM BRAINLY

if cosx+cosy+cosz=0=sinx+siny+sinz

then the possible value of cos(x-y/2)=k

then |2k|=?

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