Question #5b278

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Answer 1 · 2017-04-14T06:14:49

${tan}^{2} x + 4 sec x = 4$ $tan^2x+4secx=4$

$\Rightarrow {sec}^{2} x - 1 + 4 sec x = 4$ $=>sec^2x-1+4secx=4$

$\Rightarrow {sec}^{2} x + 4 sec x + 2^{2} = 4 + 4 + 1$ $=>sec^2x+4secx+2^2=4+4+1$

$\Rightarrow {(sec x + 2)}^{2} = 9$ $=>(secx+2)^2=9$

$\Rightarrow sec x + 2 = \pm 3$ $=>secx+2=pm3$

$sec x = 1$ $secx=1$

$\Rightarrow cos x = 1$ $=>cosx=1$

$x=2npi" where "n in ZZ$

Again

$secx=-3-2=-5$

$=>cosx=-1/5=cos(2.09rad)$

$=>x=2npipm2.09" where " n in ZZ$