Problem

a) Find the value of $m$ if $\sec 65^{\circ}=\operatorname{cosec}(2 m-15)^{\circ}$

Solution

Step 1 :Given that \(\sec 65^\circ = \operatorname{cosec}(2m - 15)^\circ\)

Step 2 :Using the identities \(\sec x = \frac{1}{\cos x}\) and \(\operatorname{cosec} x = \frac{1}{\sin x}\), we get \(\frac{1}{\cos 65^\circ} = \frac{1}{\sin (2m - 15)^\circ}\)

Step 3 :Using the identity \(\sin (2x) = 2 \sin x \cos x\), we can rewrite the equation as \(\frac{1}{\cos 65^\circ} = \frac{1}{2 \sin (m - 7.5^\circ) \cos (m - 7.5^\circ)}\)

Step 4 :Solving for m, we get \(m = 20\)

Step 5 :\(\boxed{m = 20}\)

From Solvely APP
Source: https://solvelyapp.com/problems/7198/

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