4sin2θ + 14cos2θ = 7 How to find cosθ??

Question

I understand that sin theta + cos theta = 1 but how to apply it here and solve it?
Help someone please!!??

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Answer 1 · 2018-01-08T01:58:22

#4sin2theta-7+14cos2theta=0#

#=>8sinthetacostheta-7cos^2theta-7sin^2theta+14cos^2theta-14sin^2theta=0#

#=>7cos^2theta+8sinthetacostheta-21sin^2theta=0#

#=>7+8tantheta-21tan^2theta=0#

#=>21tan^2theta-8tantheta-7=0#

#=>tan theta=(8pmsqrt(64+4*21*7))/(2xx21)#

#=>tan theta~~0.8or-0.4#

So

#costheta=pm1/sqrt(1+tan^2theta#

#costheta=pm1/sqrt(1+(0.8)^2)=pm0.78#
Again
#costheta=pm1/sqrt(1+(-0.4)^2)~~pm0.93#