Question

if sina =1/2 then find the value of Sina (Sina -coseca)

Answer 1

a=30°
sina=1/2
coseca= 2
sin a . (sina - coseca) = 1/2.(1/2-2)
=1/2. (1-4÷2)
= 1/2. -3/2
=-3/4

Answer 2

Answer:

sin a(sin a - cosec a)  = - $\frac{3}{4}$

Step-by-step explanation:

• Given, sin a = $\frac{1}{2}$
• We have to find the value of sin a(sin a - cosec a)
• We know that sin30° = $\frac{1}{2}$  and here it is mentioned sin a = $\frac{1}{2}$

        Combining these two we get, a = 30°

        So, sin a = sin30° = $\frac{1}{2}$

• For a right angle triangle, sin$\theta$ = $\frac{height}{hypotenuse}$ and cosec$\theta$ = $\frac{hypotenuse}{height}$

       So, we can write, cosec$\theta$ = 1/ sin$\theta$

                                     cosec a = cosec 30°

                                                    = 1/ sin30°

                                                    = 1/ $\frac{1}{2}$ = 2

• Putting the values of sin a and cosec a in the expression,

       sin a(sin a - cosec a) =  $\frac{1}{2}$ × ( $\frac{1}{2}$ -2)

                                         =  $\frac{1}{2}$ × ( -$\frac{3}{2}$ )

                                         = - $\frac{3}{4}$