Use an Addition or Subtraction Formula to write the expressi

Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number. tan(pi/18) + tan(pi/9)/1 - tan(pi/18) tan(pi/9) Find its exact value Write the given expression in terms of x and y only. cos(sin^-1(x)-tan^-1(y))

Solution

7)

[tanA+tanB]_{/[1-tanAtanB]}=tan(A+B)

[tan(/18)+tan(/9)]_{/[1-tan(/18)tan(/9)]}=tan((_/18)+(_/9))

[tan(/18)+tan(/9)]_{/[1-tan(/18)tan(/9)]}=tan(3_/18)

[tan(/18)+tan(/9)]_{/[1-tan(/18)tan(/9)]}=tan(_/6)

[tan(/18)+tan(/9)]_{/[1-tan(/18)tan(/9)]}=1_/3 or (3)_/3

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8)

cos(sin^-1(x) -tan^-1(y))

=cos(sin^-1(x_/1) -tan^-1(y_/1))

=[cos(sin^-1(x_/1))cos(tan^-1(y_/1))] +[sin(sin^-1(x_/1))sin(tan^-1(y_/1))]

=[cos(cos^-1((1²-x²)_/1))cos(cos^-1(1_/(1²+y²)))] +[sin(sin^-1(x_/1))sin(sin^-1(y_/(1²+y²)))]

=[((1²-x²)_/1)(1_/(1²+y²))] +[(x_/1)(y_/(1²+y²))]

=((1-x²)_/(1+y²)) +(xy_/(1+y²))

=(xy+(1-x²))_/(1+y²)