Question
Simplify: sinx+sin 3x+sin5x
Solution
We are asked to simplify the expression: sin x + sin 3x + sin 5x using product-to-sum identities . We first group the terms as follows: (sin x + sin 5x) + sin 3x Now apply the identity: sin A + sin B = 2 sin[(A + B)/2] cos[(A − B)/2] Apply this to sin x + sin 5x: A = 5x, B = x sin x + sin 5x = 2 · sin[(5x + x)/2] · cos[(5x − x)/2] = 2 · sin(3x) · cos(2x) Now substitute this back into the expression: sin x + sin 3x + sin 5x = [2 · sin(3x) · cos(2x)] + sin 3x Now factor sin 3x from both terms: = sin 3x · [2 cos 2x + 1]
A piece of ice is floating in water kept in a beaker. When all the ice melts the level of water will -
When a capacitor is fully charged in a DC circuit, the current through it is:
Frequency modulation (FM) changes:
A conducting rod of length 0.2 m is rotated with angular velocity 10 rad/s about one end in a uniform magnetic field of 0.5 T perpendicular to the plane...
The term ‘Isoneph' indicates the lines of equal –
Compared to fresh Water, the freezing point of sea water is -
‘Lubb-dupp’ sound is produced due to the action of
A soap bubble shows colours when illuminated with white light. This is due to –
If the specific heat at constant pressure Cₚ is greater than Cᵥ , the difference Cₚ -Cᵥ is equal to:
What does Ohm's Law state? Â