Maths · Inverse trigonometrical functions and their properties
If then find the value of
If \( \cos ^{-1} \lambda+\cos ^{-1} \mu+\cos ^{-1} \gamma=3 \pi \) then find the value of \( \lambda \mu+\mu \gamma+\gamma \lambda \)
- A. 1
- B. 2
- C. 3 \)
- D. 4
Step-by-step solution
The range of cos^{-1} is [0, π], so the maximum sum of three such angles is 3π, attained only when each angle equals π. Thus cos^{-1}(λ)=π, cos^{-1}(μ)=π, cos^{-1}(γ)=π, giving λ=μ=γ=-1. Then λμ+μγ+γλ = (-1)(-1)+(-1)(-1)+(-1)(-1)=1+1+1=3.
Related MCQs
- Assertion Consider =\sin ^{-1}\left(\sec \left(\tan ^{-1} \boldsymbol{x}\right)+\right. \) \right. \) Statement-1: Domain of \) is a singlet…
- If value of which satisfy equation ^{2}-3\left(\cot ^{-1} x\right)+2>0 \) is or Find the value of…
- The number of real solutions of the equation }+ \) is…
- Assertion \) If then +\cos ^{-1}(\sin x)=\pi-2 x \) Reason \cos ^{-1} x=\frac{\pi}{2}-\sin ^{-1} x \forall x \in \) \)…
- Assertion then Reason \)…