The value of 1 sin 4- - -2 - 2 tan - - -

(1) #160; #160; #160; #10; sin ( 4θ +π2 #10;)=cos 4θ #10; #10;(2) #160; #160; #160; #10; tanθ +θ =sinθ #10;cosθ+1cosθ=sinθ +1c ...

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Sign of Trigonometric Ratios in Different Quadrants

The value of ...

Question

The value of
1) $sin$ $(4 θ + \frac{π}{2})$ .
2) $tan$ $θ + sec θ$ .

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Solution

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θ

sin 7 θ = sin 4 θ - sin θ i n 0 < θ < \frac{π}{2}

θ

\frac{π}{2}

∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 + {sin}^{2} θ & {cos}^{2} θ & 4 sin 4 θ {sin}^{2} θ & 1 + {cos}^{2} θ & 4 sin 4 θ {sin}^{2} θ & {cos}^{2} θ & 1 + 4 sin 4 θ \end{matrix} ∣ ∣ ∣ ∣ ∣ = 0

θ

(- \frac{π}{2}, \frac{π}{2})

(1 - t a n θ) (1 + t a n θ) s e c^{2} θ + 2 t a n^{2} θ + 2 = 0

θ

sin 7 θ = sin 4 θ - sin θ

0 < θ < \frac{π}{2}

θ

(- π / 2, π / 2)

(1 - t a n θ) (1 + t a n θ) s e c^{2} θ + 2^{t a n^{2} θ} = 0

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