Question

tanθ+cotθ=2... if θ is an acute angle.. then the value of sin³θ+cos³θ is:-
a)1
b)1/2
c)√2/2
d) √2

Answer 1

Answer:

option c

Step-by-step explanation:

theta is 45 degree as tan 45 and cot 45 is 1 so adding both makes 2

sin 45degree ³ + cos 45 degree ³ =

(1/root2)³ +( 1/ root2 )³ =

1/ 2 root 2 + 1 / 2 root 2

2/ 2 root 2

2 can be written as root 2 × root 2

do cancelletion and get the answer as option c

Answer 2

GIVEN,

tanx+cotx=2

TO FIND,

value of sin³x+cos³x.

SOLUTION,

we are given that

tanx+cotx=2 and x is an acute angle, so this equation is only satisfied if x=45°

hence,

tan45°+cot45°= 1+1 = 2

now putting x=45°

⇒sin³45°+ cos³45°

substituting the values,

⇒ $(\frac{1}{\sqrt{2} } )^{3} + (\frac{1}{\sqrt{2} } )^{3}$

solving further,

⇒ $\frac{1}{2\sqrt{2} } +\frac{1}{2\sqrt{2} }$

⇒$\frac{2}{2\sqrt{2} }$

we know that  2=$\sqrt{2} \sqrt{2}$

⇒$\frac{\sqrt{2} *\sqrt{2} }{2\sqrt{2} }$

⇒ $\frac{\sqrt{2} }{2}$

HENCE THE VALUE OF SIN³X+COS³= √2/2.