CBSE (Science) Class 11CBSE
Share

Books Shortlist

If Sin (α + β) = 1 and Sin (α − β) = 1 2 , Where 0 ≤ α, β ≤ π 2 , Then Find the Values of Tan (α + 2β) and Tan (2α + β). - CBSE (Science) Class 11 - Mathematics

ConceptTrigonometric Functions of Sum and Difference of Two Angles

Question

If sin (α + β) = 1 and sin (α − β) $= \frac{1}{2}$, where 0 ≤ α, $\beta \leq \frac{\pi}{2}$, then find the values of tan (α + 2β) and tan (2α + β).

Solution

Given:
$\sin (\alpha + \beta) = 1\text{ and }\sin (\alpha - \beta) = \frac{1}{2}$
$\Rightarrow \alpha + \beta = 90^\circ . . . (1)$
$and \alpha - \beta = 30^\circ . . . (2)$
By adding eq (1) and eq (2) we get:
$2\alpha = 120^\circ$
$\Rightarrow \alpha = 60^\circ$
By subtracting eq (2) from eq (1), we get:
$2\beta = 60^\circ$
$\Rightarrow \beta = 30^\circ$
Therefore,
$\tan(\alpha + 2\beta) = \tan \left( 60^\circ + 2 \times 30^\circ \right) = \tan 120^\circ = - \sqrt{3}$
$\tan(2\alpha + \beta) = \tan \left( 2 \times 60^\circ + 30^\circ \right) = \tan 150^\circ = - \frac{1}{\sqrt{3}}$

Is there an error in this question or solution?

APPEARS IN

RD Sharma Solution for Mathematics Class 11 (2019 to Current)
Chapter 7: Values of Trigonometric function at sum or difference of angles
Ex.7.10 | Q: 26 | Page no. 21
Solution If Sin (α + β) = 1 and Sin (α − β) = 1 2 , Where 0 ≤ α, β ≤ π 2 , Then Find the Values of Tan (α + 2β) and Tan (2α + β). Concept: Trigonometric Functions of Sum and Difference of Two Angles.
S