JIPMAT 2024Geometry > HardBoth Statement I and Statement II are trueBoth Statement I and Statement II are falseStatement I is true but Statement II is falseStatement I is false but Statement II is true✅ Correct Option: 1Related questions:If sinθ+cosθsinθ−cosθ=3\frac{\sin\theta + \cos\theta}{\sin\theta - \cos\theta} = 3sinθ−cosθsinθ+cosθ=3, then value of sin4θ−cos4θ\sin^4\theta - \cos^4\thetasin4θ−cos4θ isWhich of the following trigonometric identities are true? sin2(41∘)+sin2(49∘)=1sin2(60∘)−2tan(45∘)−cos2(30∘)=−1sin2(θ)+11+tan2(θ)=1\begin{aligned} & \sin ^2\left(41^{\circ}\right)+\sin ^2\left(49^{\circ}\right)=1 \\ & \sin ^2\left(60^{\circ}\right)-2 \tan \left(45^{\circ}\right)-\cos ^2\left(30^{\circ}\right)=-1 \\ & \sin ^2(\theta)+\frac{1}{1+\tan ^2(\theta)}=1 \end{aligned}sin2(41∘)+sin2(49∘)=1sin2(60∘)−2tan(45∘)−cos2(30∘)=−1sin2(θ)+1+tan2(θ)1=1Two ships are sailing in the sea on the two sides of a lighthouse. The angles of elevation of the top of the lighthouse as observed from two ships are 30° and 45°, respectively. If the lighthouse is 100 m high, the distance between two ships is approximately: