IIT-JEE 1981Question 1
Let the angles $A,B,C$ of a triangle $ABC$ be in A.P. and let $b:c=\sqrt3:\sqrt2$. Find the angle $A$.
Trigonometric Ratio & Identities
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IIT-JEE 1979Question 2
(a) Draw the graph of $y=\dfrac{1}{\sqrt2}(\sin x+\cos x)$ from $x=-\dfrac{\pi}{2}$ to $x=\dfrac{\pi}{2}$.
(b) If $\cos(\alpha+\beta)=\dfrac45$, $\sin(\alpha-\beta)=\dfrac{5}{13}$, and $\alpha,\beta$ lie between $0$ and $\dfrac{\pi}{4}$, find $\tan2\alpha$.
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IIT-JEE 1982Question 3
A vertical pole stands at a point $Q$ on a horizontal ground. $A$ and $B$ are points on the ground, $d$ meters apart. The pole subtends angles $\alpha$ and $\beta$ at $A$ and $B$ respectively. $AB$ subtends an angle $\gamma$ at $Q$. Find the height of the pole.
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IIT-JEE 1979Question 4
(a) A balloon is observed simultaneously from three points $A$, $B$ and $C$ on a straight road directly beneath it. The angular elevation at $B$ is twice that at $A$ and the angular elevation at $C$ is thrice that at $A$. If the distance between $A$ and $B$ is $a$ and the distance between $B$ and $C$ is $b$, find the height of the balloon in terms of $a$ and $b$.
(b) Find the area of the smaller part of a disc of radius $10$ cm, cut off by a chord $AB$ which subtends an angle of $22\tfrac12^\circ$ at the circumference.
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IIT-JEE 1978Question 5
If $\tan\alpha=\dfrac{m}{m+1}$ and $\tan\beta=\dfrac{1}{2m+1}$, find the possible values of $(\alpha+\beta)$.
Trigonometric Ratio & Identities
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