Solving the Tricky Math Problem: Find sin2x

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The discussion revolves around solving the equation sin x + cos x + tan x + cosec x + sec x + tan x + cot x = 8 to find sin 2x. Participants emphasize the importance of rewriting all trigonometric functions in terms of sine and cosine to simplify the problem. There is a concern about the accuracy of the equation, particularly regarding the repetition of tan x and the total number of terms. By expressing each term as a ratio, it becomes possible to combine them over a common denominator and apply trigonometric identities for simplification. Ensuring the problem is copied correctly is crucial for finding a viable solution.
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Homework Statement




sin x+cos x + tan x + cosec x + sec x+tan x +cot x = 8

find sin2x=?

i still have no idea to deal with this problem, hint please
 
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Look up the identities for rewriting cos tan etc in terms of sin.
 
Write out each term that isn't sin x or cos x in terms of its definition as a ratio of sine and/or cosine. (Does tan x really appear twice? How many terms are there supposed to be? Is this copied correctly? I ask so we don't waste time trying to solve the wrong problem... Are you sure this isn't

[sin x·cos x] + tan x + cosec x + [sec x·tan x] + cot x , for instance?)

You will now have a set of terms that you can add as fractions by putting everything over a common denominator. You will be able to make some simplifications in the numerator using trig identities. You should end up with something easier to work with. (But make sure this is copied right, or a solution will be truly hopeless...)
 

Thread 'Find the polar form of a complex number'

The working out suggests first equating ## \sqrt{i} = x + iy ## and suggests that squaring and equating real and imaginary parts of both sides results in ## \sqrt{i} = \pm (1+i)/ \sqrt{2} ## Squaring both sides results in: $$ i = (x + iy)^2 $$ $$ i = x^2 + 2ixy -y^2 $$ equating real parts gives $$ x^2 - y^2 = 0 $$ $$ (x+y)(x-y) = 0 $$ $$ x = \pm y $$ equating imaginary parts gives: $$ i = 2ixy $$ $$ 2xy = 1 $$ I'm not really sure how to proceed from here.
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