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if cosx=-12/13 and tany =8/15, pi/2<x<pi, pi<x<3pi/2 evaluate the following

a) cos(x-y) b)tan2x

In QII, we have

sinx = -5/13
tanx = -5/12
siny = -8/17
cosy = -15/17

cos(x-y) = cosx cosy + sinx siny

tan2x = 2tanx/(1 - tan^2 x)

Now plug in your numbers

Did you know?

Did you know that trigonometric functions, like cosine and tangent, can be used to evaluate complex expressions? For example, if we are given that cos(x) is equal to -12/13 and tan(y) is equal to 8/15, with x between pi/2 and pi, and y between pi and 3pi/2, we can find the values of cos(x-y) and tan(2x). To find cos(x-y), we can use the identity cos(x-y) = cos(x)cos(y) + sin(x)sin(y). From the given information, we can substitute the values of cos(x) and tan(y) into the formula and evaluate the expression. To find tan(2x), we can use the identity tan(2x) = 2tan(x)/(1-tan^2(x)). By substituting the value of tan(x) (which can be found using the given information) into the formula, we can evaluate tan(2x) and solve the expression. By using trigonometric identities and given values, we can find the values of cos(x-y) and tan(2x), making trigonometry a powerful tool in solving complex mathematical problems.