Question

if sinx+cosecx=2 where x is acute angle then the value of sin³x+ cosec³x is equal to​

Answer 1

Answer:

Step-by-step explanation:

We have,

$\tt{sin(x)+cosec(x)=2\,\,\,\,\,\,...(1)}$

$\tt{\implies\,\left\{sin(x)+cosec(x)\right\}^3=\left(2\right)^3}$

$\tt{\implies\,sin^3(x)+cosec^3(x)+3\cdot\,sin(x)\cdot\,cosec(x)\cdot\left\{sin(x)+cosec(x)\right\}=8}$

$\tt{\implies\,sin^3(x)+cosec^3(x)+3\cdot\,sin(x)\cdot\dfrac{1}{sin(x)}\cdot\left(2\right)=8\,\,\,\,\,\,\,\,\,[from\,\,(1)]}$

$\tt{\implies\,sin^3(x)+cosec^3(x)+3\cdot1\cdot2=8}$

$\tt{\implies\,sin^3(x)+cosec^3(x)+6=8}$

$\tt{\implies\,sin^3(x)+cosec^3(x)=8-6}$

$\tt{\implies\,sin^3(x)+cosec^3(x)=2}$