If $$f(x)=ax+b$$,a$$0$$ such that f:[−$$1$$,$$1$$]→[$$0$$,$$2$$], then $$cot$$⁡$$cot$$−$$1$$⁡$$7+$$$$cot$$−$$1$$⁡$$8+$$$$cot$$−$$1$$⁡$$18$$ is equal to

Question

If $$f(x)=ax+b$$,a>$$0$$ such that f:[−$$1$$,$$1$$]→[$$0$$,$$2$$], then $$cot$$⁡$$cot$$−$$1$$⁡$$7+$$$$cot$$−$$1$$⁡$$8+$$$$cot$$−$$1$$⁡$$18$$ is equal to

Infinity Learn · Accepted Answer

Given that $$f(x)=ax+b$$ Differentiating with respect to x on both sides ⇒f′(x)=a$$>$$0$$∴$$f(x) is an increasing function. ⇒$$f($$−$$1)=0$$ and $$f(1)=2$$−$$a+b=0$$ and $$a+b=2$$⇒$$a=b=1$$∴$$f(x)=x+1$$ Now, $$cot$$⁡$$cot$$−$$1$$⁡$$7+$$$$cot$$−$$1$$⁡$$8+$$$$cot$$−$$1$$⁡$$18=$$$$cot$$⁡$$tan$$−$$1$$⁡$$17+$$$$tan$$−$$1$$⁡$$18+$$$$tan$$−$$1$$⁡$$118=$$$$cot$$⁡$$tan$$−$$1$$⁡$$17+181$$−$$17$$⋅$$18+$$$$tan$$−$$1$$⁡$$118=$$$$cot$$⁡$$tan$$−$$1$$⁡$$1555+$$$$tan$$−$$1$$⁡$$118=$$$$cot$$⁡$$tan$$−$$1$$⁡$$311+$$$$tan$$−$$1$$⁡$$118=$$$$cot$$⁡$$tan$$−$$1$$⁡$$311+1181$$−$$311$$⋅$$118=$$$$cot$$⁡$$tan$$−$$1$$⁡$$65195=$$$$cot$$⁡$$tan$$−$$1$$⁡$$13=$$$$cot$$⁡$$cot$$−$$1$$⁡$$3=3=1+2=f(2)$$

$If f (x) = a x + b, a > 0 such that f : [- 1, 1] \to [0, 2], then$ $\cot [\cot^{- 1} 7 + \cot^{- 1} 8 + \cot^{- 1} 18] is equal to$

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

If f(x)=ax+b,a>0 such that f:[−1,1]→[0,2], then cot⁡cot−1⁡7+cot−1⁡8+cot−1⁡18 is equal to

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

$If f (x) = a x + b, a > 0 such that f : [- 1, 1] \to [0, 2], then$ $\cot [\cot^{- 1} 7 + \cot^{- 1} 8 + \cot^{- 1} 18] is equal to$