Question

Please solve this question!!!!!!​

Answer 1

sin²x + cos²30 = 5/4

cos 30 = √3/2

⇒ cos²30 = 3/4

sin²x = 5/4 - 3/4

⇒ sin²x = ( 5 - 3 )/4

⇒ sin²x = 2/4

⇒ sin x = 1/√2

⇒ sin x = sin 45

⇒ x = 45°

x = 45° .

b )

$\sqrt{\frac{5}{3}}^{x-8}=(\frac{27}{125})^{2x-3}$

$\implies (\frac{5}{3})^{(x-8)/2}=(\frac{5}{3})^{(-3)(2x-3)}$

$\\\\\implies x-8=(-6)(2x-3)\\\\\implies x-8=-12x+18\\\\\implies x+12x=18+8\\\\\implies 13x=26\\\\\implies x=26/13\\\\\implies x=2$

Answer 2

#lordcarbin

((((1))))

sin^2x+cos^2 30°=5/4

cos30°=√3/2

so sin^2x=5/4-(√3/2)^2

sin^2x=5/4-3/4

sinx=√1/2

sinx=1/√2

as we know sin45°=1/√2

so

therefore

sinx=sin45°

x=45°

((((2))))

x=2

see the attachment for the steps.

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