7 Sin² theta + 3 Cos² theta = 4

find the value of Sec² theta

[tex]7\sin^{2}\theta\:+\:3\cos^{2} \theta\:=\:4

1 thought on “7 Sin² theta + 3 Cos² theta = 4<br /><br />find the value of Sec² theta<br /><br />[tex]7\sin^{2}\theta\:+\:3\cos^{2} \theta\:=\:4”

1. Answer:

   7sin

   2

   θ+3cos

   2

   θ=4

   ⇒7sin

   2

   θ+3(1−sin

   2

   θ)=4

   ⇒7sin

   2

   θ+3−3sin

   2

   θ=4

   ⇒4sin

   2

   θ=1

   ⇒sin

   2

   θ=

   4

   1

   ⇒sinθ=

   2

   1

   ⇒sinθ=sin30

   ∘

   ⇒θ=30

   ∘

   L.H.S =secθ+cosecθ

   =sec30

   ∘

   +cosec30

   ∘

   =

   3

   2

   +2

   = R.H.S

   Hence proved.

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