Question

Evaluate
i) sin (2 sin ^-1(-4/5))​

Answer 1

Answer:

24/25

Step-by-step explanation:

Sin[2 sin-1(4/5)].

we know the formula that

2sin-1x=sin-1(2x√1-x^)

sin[sin-1(8/5)√1-16/25]

sin [sin-1(8/5×3/5)]=sin(sin-1(24/25)]=24/25

Answer 2

Answer:

The value of the given expression is

$\sin(2 \sin {}^{ - 1} ( \frac{4}{5} ) ) = \frac{24}{25}$

Step-by-step explanation:

The given expression is

$\sin(2 \sin {}^{ - 1} ( \frac{4}{5} ) )$

Let us solve this by substitution method as follows

$\sin {}^{ - 1} ( \frac{4}{5} ) = \alpha = > \sin( \alpha ) = \frac{4}{5}$

Therefore,

$\cos( \alpha ) = \sqrt{1 - { \sin {}^{2} ( \alpha ) } } \\ = \sqrt{1 - ({ \frac{4}{5} })^{2} } = \sqrt{ \frac{9}{25} } = \frac{3}{5}$

Now we have

$\sin(2 \sin {}^{ - 1} ( \frac{4}{5} ) ) = \sin(2 \alpha ) \\ = 2 \sin( \alpha ) \cos( \alpha ) \\ = 2 \times \frac{4}{5} \times \frac{3}{5} = \frac{24}{25}$

Therefore,the value of the given expression us

$\sin(2 \sin {}^{ - 1} ( \frac{4}{5} ) ) = \frac{24}{25}$

#SPJ3