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

Question

Accepted Answer

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})

Answer

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})

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

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