Introduction to Trigonometry
CH08 Question Bank
CBSE_CH08_QUESTION_BANK
Grade 10
Question:
If $A=B=45^\circ$, verify that $\cos(A+B) = \cos A \cos B - \sin A \sin B$.
Step-by-Step Solution
Key Concept: Evaluate both sides independently using standard values and compare.
LHS: $\cos(45^\circ+45^\circ)=\cos90^\circ=0$. [1.0 Mark]
RHS: $\cos45^\circ\cos45^\circ-\sin45^\circ\sin45^\circ=\dfrac{1}{\sqrt2}\times\dfrac{1}{\sqrt2}-\dfrac{1}{\sqrt2}\times\dfrac{1}{\sqrt2}=\dfrac12-\dfrac12=0$. [1.0 Mark]
Since LHS $=$ RHS $=0$, the relation is verified for $A=B=45^\circ$. [1.0 Mark]
Correct Answer:
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