Question

sec 4x = cosec (3x-43) then x=?​

Answer 1

Question:

If sec4x = cosec(3x-43°), then find x = ?

Solution:

We know that;

sec@ = cosec(90°-@)

Thus,

=> sec4x = cosec(3x-43°)

=> cosec(90°-4x) = cosec(3x-43°)

=> 90° - 4x = 3x - 43°

=> 3x + 4x = 90° + 43°

=> 7x = 133°

=> x = 133°/7

=> x = 19°

Hence,

The required value of x is 19°.

Answer 2

$\huge\bf{Solution}\\ \\ \bf{Given \: that}, \\ \\ \implies \: \bf{sec4x = cosec(3x - 43) }\\ \\ \bf{we \: know \: that },\\ \\ \bf \red{ \star \: cosec(90 - \theta) = sec \theta} \\ \\ \implies \: \bf{cosec(90 - 4x) = cosec(3x - 43)} \\ \\ \implies \: \bf{90 - 4x = 3x - 43} \\ \\ \implies \: \bf{90 + 43 = 4x + 3x }\\ \\ \implies \: \bf{133 = 7x }\\ \\ \implies \: \bf{x = \frac{133}{7} } \\ \\ \implies \: \bf{\boxed{ x = 19}}$