If ( a cos theta b sin theta m ) and ( a sin theta b cos theta n ) prove that ( a 2 b 2 m 2 n 2 ) - Given:( a cos theta+b sin theta=m ) and ( a sin theta-b cos theta=n )To do:We have to prove that ( a^{2}+b^{2}...
cos ( x - \frac{\pi}{3}) + sin(\frac{\pi}{6} - x) = cos\ x Prove the identity: 2sin^(-1)(x) = cos^(-1)(1 - 2x^2), x greater than or equal to 0. Prove where n_1\sin i = n_2\sin \theta. \frac{2n_1\cos i}{n_2 \cos i +...
Example: Consider an experiment E=Tossing a coin. We can only have as an outcome/event, Heads, Tails If we assign/calculate that the probability that Head occurs is P(H)=12, then Probability that heads doesn't occur ( an event that complements the previous event) can be given as P(H...
If f(x)=2sinx+3xx, find f′(3) Logarithmic Derivative: When we have one function elevated to another, we apply the logarithmic derivative. Step step, from applying logarithm on both sides and calculating the derivative on both sides, we have: h(x)=m(x)n(x)lnh(x)=ln...
If ( sin theta frac a b ) find ( sec theta tan theta ) in terms of ( a ) and ( b ) - Given:( sin theta=frac{a}{b} ).To do:We have to find the value of ( sec theta+tan theta ).Solution: Let, in a triangle $ABC$ right-angled at $B$, $ si...
If ( sec theta frac 5 4 ) find the value of ( frac sin theta 2 cos theta tan theta cot theta ) - Given:$sec theta = frac{5}{4}$.To do:We have to find the value of ( frac{sin theta-2 cos theta}{tan theta-cot theta} ).Solution: Let, in ...
If cot theta frac 7 8 evaluate frac (1 sin theta)(1 sin theta) (1 cos theta)(1 cos theta) - Given :The given term is $cot theta=frac{7}{8}$.To do :We have to evaluate $ frac{(1+sin theta)(1-sin theta)}{(1+cos theta)(1-cos theta...