Question

A projectile is fired with a constant speed at two different angles of projection, say $\alpha$ and $\beta$, that give it the same range. Then, α and β are such that,

• A. $cosec\alpha =sec\beta$
• B. $tan(\alpha +\beta )\to \infty$
• C. $si{n}^2\alpha –cos2\alpha =si{n}^2\beta –co{s}^2\beta$
• D. $si{n}^2\alpha +co{s}^2\alpha =si{n}^2\beta +co{s}^2\beta$

Answer 1

Answer: (A), (B), (D)

The correct options are
A $cosec\alpha =sec\beta$
B $tan(\alpha +\beta )\to \infty$
D $si{n}^2\alpha +co{s}^2\alpha =si{n}^2\beta +co{s}^2\beta$

For the same range, $\alpha +\beta ={90}^{\circ }$ (or ) $\beta ={90}^{\circ }-\alpha$. Choices a), b) and d) are correct as they satisfy these relations.