jika cot 48°= 1/a, maka sec 4° = mohon bantuannya

[tex]\displaystyle \cot49^\circ=\frac1a\\\frac{x}{y}=\frac1a\\\therefore\\x=1\\y=a\\\\\sec4^\circ=\frac{1}{\cos4^\circ}\\\sec4^\circ=\frac{1}{\cos(49^\circ-45^\circ)}\\\sec4^\circ=\frac{1}{\cos49^\circ\cos45^\circ+\sin49^\circ\sin45^\circ}\\\sec4^\circ=\frac{1}{\frac{\sqrt2}{2\sqrt{a^2+1}}+\frac{a\sqrt2}{2\sqrt{a^2+1}}}\\\sec4^\circ=\frac{2\sqrt{a^2+1}}{\sqrt2(1+a)}\\\sec4^\circ=\frac{\sqrt2\cdot\sqrt{a^2+1}}{1+a}\\\boxed{\boxed{\sec4^\circ=\frac{\sqrt{2a^2+2}}{1+a}}}[/tex]

Mapel : Matematika
Kelas : X SMA
Bab : Trigonometri

Pembahasan :
Cot 49° = 1/a
1/tan 49° = 1/a
Tan 49° = a

Tan (45 + 4)° = (Tan 45 + Tan 4)/(1 - tan 45. Tan 4)
a = (1 + Tan 4)/(1 - aTan 4)
a - a²Tan 4 = 1 + Tan 4
a²Tan 4 + Tan 4 = a - 1
Tan 4(a² + 1) = a - 1
Tan 4 = (a - 1)/(a² + 1)

Ingat !
Tan A° = Depan/Samping
Tan 4° = (a - 1)/(a² + 1)

Depan = a - 1
Samping = a² + 1
Miring = √[(a² + 1)² + (a - 1)²] = √[a⁴ + 3a² - 2a + 2]

Maka...
Sec 4° = 1/Cos 4
Sec 4° = 1/[(a² + 1)/{√(a⁴ + 3a² - 2a + 2}]
Sec 4° = [√(a⁴ + 3a² - 2a + 2)]/(a² + 1)