Wykorzystując dane  oblicz wartość wyrażenia   Dane: przeciwprostokątna-√ 7 przyprostokątna przyległa- √ 3   a) 4*sin² α * cos²α + tg²α *ctg²α b) (sin α +tg α)²

Dane:   c = √ 7 a = √ 3 b = ? sinα = ? cosα= ? tgα= ? ctgα= ?   sinα = a/c   cosα =b/c   tgα = a/b   ctgα = b/a     a² + b² = c²   b² = c² - a²   b² = (√ 7)² - (√3)²   b² = 7 - 3   b² = 4   b = √4   b = 2   sinα = a/c = √ 3/√ 7 = √ 21/7   cosα =b/c = 2/√ 7 = 2/√ 7    tgα = a/b =  √ 3/2   ctgα = b/a = 2/√ 3 = 2√ 3/3    a)    4*sin² α * cos²α + tg²α *ctg²α = 4*(sinα*cosα)² + (tgα*ctgα)² =                                                 = 4*(√ 21/7*2/√ 7)² + 1² =                                                 = 4*(2√3/7)² + 1 =                                                 = 4*4*3/49 + 1 =                                                = 48/49 + 1 =                                                = 1  48/49    4*(√ 21/7)²*(2/√ 7)²  b)   (sin α +tg α)² = (√ 21/7 + √ 3/2)² =                        =  (√ 21/7)² + 2*√ 21/7*√ 3/2  + (√ 3/2)² =                        = 21/49 + √ 63 + 3/2 =                        = 3/7 + 3√ 7 + 3/2 =                        = 6/14 + 21/14 + 3√ 7 =                        = 3√ 7 + 27/14