Question

Se cosx. senx = √3/2 e tg x = √2, 0 < x < π, calcule o único valor de senx + sec x

Answer 1

Resposta:

Explicação passo-a-passo:

cos x. sen x = √3/2

tg x = √2

(sen x/cos x)² = (√2)²

sen² x/cos² x = 2

sen² x = 2cos² x

sen² x + cos² x = 1

2cos² x + cos² x = 1

3cos² x = 1

cos² x = 1/3

√cos² x = √1/3

cos x = 1/√3

cos x = (1/√3)(√3/√3)

cos x = √3/3

cos x. sen x = √3/2

√3/3. sen x = √3/2

sen x = 3√3/2

sec x = 1/cos x

sen x + sec x =

sen x + 1/cos x =

3√3/2 + 1/√3/3 =

3√3/2 + 3/√3 =

3√3/2 + 3√3/3 =

3√3/2 + √3 =

√3(3/2 + 1) =

√3(3/2 + 2/2) =

√3(5/2) =

5√3/2.