Using trig identities to cancel and simplify equations

I have included all details on attached file. Please help me get to the final line of the question. Many thanks

Tangent sum formulas

Explain why tan(x + 450 degrees) cannot be simplified using the tangent sum formulas but can be simplified by using the sine and cosine formulas. (Please show all work).

Trigonometry

What is the difference between a trig equation that is an identity and a trig equation that is not an identity? Provide an example to clarify.

Solving a quartic equation

I can not factor or group this to set it equal to zero to determine the solution. Can you help me? 4x^4-65x^2+16=0

Trigonometry

--- (See attached file for full problem description)

Degrees and angles

For the given triangle, side a =7.0, side b= 4.0 and side c = 6.0 what is the size in degrees of the angle b( the angle opposite side b)?

Converting Polar Coordinates to Rectangular Coordinates : (r,degrees)= (-5,-55 degrees)

Find the rectangular cordinates of the point (r,degrees)= (-5,-55 degrees)

Civil Engineering and Construction Pathways : Length of an Arc and Volume of Dirt

a. The diagram over shows an area of a railway cutting that has failed in the form of a shallow rotational slip. Using radians as a measure of angular displacement determine the length of the failure surface AB. b. A partially completed site survey of a quadrilateral site is given below. You are responsible for ordering ...continues

In the movie Close Encounters of Third Kind, there was a scene where the star

In the movie Close Encounters of Third Kind, there was a scene where the star, Richard Dreyfuss, was approaching Devil’s Tower in Wyoming. He could have determined his distance from Devil’s Tower by first stopping at point P, and taken a measurement of the angle from his location to the height of the tower of 13.5 degrees. He ...continues

Calculation of distance from trigonometry

In the movie Close Encounters of Third Kind, there was a scene where the star, Richard Dreyfuss, was approaching Devil's Tower in Wyoming. He could have determined his distance from Devil's Tower by first stopping at point P, and taken a measurement of the angle from his location to the height of the tower of 13.5 degrees. He ...continues