Question

If a=sin(π/4), b=cos(π/4) & c=-cosec(π/4). Then a^3 + b^3 + c^3 = ?​

Answer 1

Answer:

5/(2)^0.5 .

$5 \div \sqrt{2}$

Answer 2

Given,

• a= sin π/4
• b = cos π/4
• c = -cosec π/4

To find,

• We have to find the value of $a^3 +b^3 +c^3$.      (1)

Solution,

If a =sin(π/4), b=cos(π/4) & c=-cosec(π/4) then $a^3 +b^3 +c^3$ is  $-3/\sqrt{2}$.

As we know that,

sin π/4 = 1/$\sqrt{2}$ , cos π/4 = 1/$\sqrt{2}$, cosec  π/4 = $\sqrt{2}$,

Substituting the above values in (1), we get

       (sin π/4)³ + (cos π/4)³ + ( -cosec π/4)³

           (1/$\sqrt{2}$)³ +   (1/$\sqrt{2}$)³  + (- $\sqrt{2}$)³

              1/2$\sqrt{2}$ + 1/2$\sqrt{2}$ -2$\sqrt{2}$

Taking $2\sqrt{2}$ as LCM, we get

             $2 -8/2\sqrt{2}$

                $-6/2\sqrt{2}$

                 $-3/\sqrt{2}$

Hence, if a =sin(π/4), b=cos(π/4) & c=-cosec(π/4) then $a^3 +b^3 +c^3$ is  $-3/\sqrt{2}$.