Question

If 2 sin(2x – 15) = √3 then find the value of
sin2(2x + 10) + tan2(x + 5).​

Answer 1

Step-by-step explanation:

In pic : convert the angle from radian to degree

Answer 2

Answer:

${sin}^{2} (2x + 10) + {tan}^{2} (x + 5) = \frac{13}{12}$

Step-by-step explanation:

*Note: There is a correction in question.

If 2 sin(3x – 15) = √3 then find the value of sin^2(2x + 10) + tan^2(x + 5).

first find the value of x,for that from the given condition

$2 \sin(3x - 15) = \sqrt{3} \\ \\ \sin(3x - 15) = \frac{ \sqrt{3} }{2} \\ \\ \sin(3x - 15) = \sin(60) \\ \\ 3x - 15 = 60 \\ \\ 3x = 75 \\ \\ x = \frac{75}{3} \\ \\ x = 25$

Now,

${sin}^{2} (2x + 10) + {tan}^{2} (x + 5) \\ \\ {sin}^{2} (2 \times 25 + 10) + {tan}^{2} (25 + 5) \\ \\ {sin}^{2} (60) + {tan}^{2} (30) \\ \\ \bigg ({ \frac{ \sqrt{3} }{2} }\bigg)^{2} + \bigg({ \frac{1}{\sqrt{3}} }\bigg)^{2} \\ \\ = \frac{3}{4} + \frac{1}{3} \\ \\ = \frac{9 + 4}{12} \\ \\ = \frac{13}{12} \\ \\ {sin}^{2} (2x + 10) + {tan}^{2} (x + 5) = \frac{13}{12}$

Hope it helps you.