Question

√2 sin^2 38° +3+2 sin^2 52°
/
√3 cosec^2 17° -2-3 tan^2 73°

equals to
1. 5
2. √5
3. 1
4. 1/5
​

Answer 1

Trigonometry:

    Trigonometry is the study of relations between angles and their ratios with various properties to find sine, cosine, tan, cosec, sec and cot ratios. Some properties can deduce angles in their general value apart from known definite ones. Now let us know some identities-

    1. sin²θ + cos²θ = 1

    2. sec²θ - tan²θ = 1

    3. cosec²θ - cot²θ = 1

    4. sin(90° - θ) = cosθ

    5. tan(90° - θ) = cotθ

Answer:

    Required value = √5

Step-by-step explanation:

Now, $\mathsf{\sqrt{\frac{2sin^{2}38^{\circ}+3+2sin^{2}52^{\circ}}{3cosec^{2}17^{\circ}-2-3tan^{2}73^{\circ}}}}$

    $\mathsf{=\sqrt{\frac{2sin^{2}38^{\circ}+3+2\{sin(90^{\circ}-38^{\circ})\}^{2}}{3cosec^{2}17^{\circ}-2-3\{tan(90^{\circ}-17^{\circ})\}^{2}}}}$

    $\mathsf{=\sqrt{\frac{2sin^{2}38^{\circ}+3+2cos^{2}38^{\circ}}{3cosec^{2}17^{\circ}-2-3cot^{2}17^{\circ}}}}$

    $\mathsf{=\sqrt{\frac{2(sin^{2}38^{\circ}+cos^{2}38^{\circ})+3}{3(cosec^{2}17^{\circ}-cot^{2}17^{\circ})-2}}}$

    $\mathsf{=\sqrt{\frac{2+3}{3-2}}}$

    = √5

Answer 2

Step-by-step explanation:

What is the work required to increase the velocity of car from 36 km/h to 108 km/h, if the mass of the car is 1200 kg?