## Active forum topics

- General Solution of $y' = x \, \ln x$
- engineering economics: construct the cash flow diagram
- Eliminate the Arbitrary Constants
- Law of cosines
- Maxima and minima (trapezoidal gutter)
- Special products and factoring
- Integration of 4x^2/csc^3x√sinxcosx dx
- application of minima and maxima
- Sight Distance of Vertical Parabolic Curve
- Application of Differential Equation: Newton's Law of Cooling

## New forum topics

- General Solution of $y' = x \, \ln x$
- engineering economics: construct the cash flow diagram
- Integration of 4x^2/csc^3x√sinxcosx dx
- Maxima and minima (trapezoidal gutter)
- Special products and factoring
- Newton's Law of Cooling
- Law of cosines
- Can you help me po to solve this?
- Eliminate the Arbitrary Constants
- Required diameter of solid shaft

## Recent comments

- Use integration by parts for…3 weeks 2 days ago
- need answer3 weeks 2 days ago
- Yes you are absolutely right…3 weeks 5 days ago
- I think what is ask is the…3 weeks 5 days ago
- $\cos \theta = \dfrac{2}{…3 weeks 6 days ago
- Why did you use (1/SQ root 5…3 weeks 6 days ago
- How did you get the 300 000pi3 weeks 6 days ago
- It is not necessary to…4 weeks ago
- Draw a horizontal time line…1 month ago
- Mali po ang equation mo…1 month 1 week ago

## Re: plane trigonometry

Prove the identity

$\dfrac{2\sin x - 2\cos x}{\tan x - \cot x} = \dfrac{\sin 2x}{\sin x + \cos x}$

$\dfrac{2(\sin x - \cos x)}{\dfrac{\sin x}{\cos x} - \dfrac{\cos x}{\sin x}} = \dfrac{\sin 2x}{\sin x + \cos x}$

$\dfrac{2(\sin x - \cos x)}{\dfrac{\sin^2 x- \cos^2 x}{\sin x \, \cos x}} = \dfrac{\sin 2x}{\sin x + \cos x}$

$\dfrac{2(\sin x - \cos x)\sin x \, \cos x}{\sin^2 x- \cos^2 x} = \dfrac{\sin 2x}{\sin x + \cos x}$

$\dfrac{2(\sin x - \cos x)\sin x \, \cos x}{(\sin x - \cos x)(\sin x + \cos x)} = \dfrac{\sin 2x}{\sin x + \cos x}$

$\dfrac{2\sin x \, \cos x}{\sin x + \cos x} = \dfrac{\sin 2x}{\sin x + \cos x}$

$\dfrac{\sin 2x}{\sin x + \cos x} = \dfrac{\sin 2x}{\sin x + \cos x}$

## Re: plane trigonometry

In reply to Re: plane trigonometry by Jhun Vert

thank you sir.may i ask u another math problem? in right triangle , C= 90 degree, B= 60 degree, A= 30degree how will you find the length of the hypotenuse (c)? thanks sir

## Re: plane trigonometry

since the given triangle is a right triangle, that is, C=90 degrees... the sum of A + B = C... denotes it... hypotenuse can be solve, one of the legs, either side "a" (opposite to angle A) or side "b" (opposite to angle B) must be known... proceed solving hypotenuse "h" (opposite to angle C=90 deg)... and use either cosine or sine function.

## Re: plane trigonometry

better for you to solve it first... and show us your solution... that's the time we will help you...

## Re: plane trigonometry

In reply to Re: plane trigonometry by Orion1213

h= opposite side over 90 degree ( but the length of the opposite side is not given) that's my dilemma sir,either of the side is not given...

## Re: plane trigonometry

In reply to Re: plane trigonometry by james perez

how to get then the length of the opposite side and adjacent f only the length of angle A,B,C were given?