Paste your question to our Mathbee AI Mentor below to get an instant step-by-step solution.
Inverse Trigonometric Functions
NCERT Exemplar Class 12
CBSE
Grade 12
Question:
Show that for any $x \in [-1, 1]$: (i) $\sin^{-1}(-x) = -\sin^{-1} x$ (ii) $\cos^{-1}(-x) = \pi - \cos^{-1} x$ (iii) $\tan^{-1}(-x) = -\tan^{-1} x$, for $x \in \mathbb{R}$.
Step-by-Step Solution
Proof of (i) $\sin^{-1}(-x) = -\sin^{-1} x$. [1.5 Marks] Proof of (ii) $\cos^{-1}(-x) = \pi - \cos^{-1} x$. [2.0 Marks] Proof of (iii) $\tan^{-1}(-x) = -\tan^{-1} x$. [1.5 Marks]
--- 🎯 Official CBSE Marking Scheme: Proving sine inverse odd property: 1.5 Marks Proving cosine inverse complement property: 2.0 Marks Proving tangent inverse odd property: 1.5 Marks
Correct Answer:
Mathbee AI Mentor (Free Demo)
Confused by the solution? Ask the AI to explain a specific step, tell you where you went wrong, or break down the key trap in this question.
Master Inverse Trigonometric Functions with Mathbee
Practice this topic under real exam conditions with strict timers, or ask our AI Mentor to explain the concepts step-by-step.