If A, B and C are the interior angles of a △ABC, show that : (i) cos A + B/2 = sin C/2 (ii) tan C + A/2 = cot B/2.

(i) Given, A, B and C are the interior angles of a △ABC. ∴ A + B + C = 180° ⇒ ⇒ To prove, cos = sin Substituting value of in L.H.S. of the equation we get : Since, L.H.S. = R.H.S. Hence, proved that cos = sin . (ii) Given, A, B and C are the interior angles of a △ABC. ∴ A + B + C = 180° ⇒ ⇒ To prove, tan = cot Substituting value of in L.H.S. of equation we get : Since, L.H.S. = R.H.S. Hence, proved that tan = cot .

Find the value of θ (0° < θ < 90°) if :
cos 63° sec (90° - θ) = 1

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Find the value of θ (0° < θ < 90°) if :
tan 35° cot (90° - θ) = 1.

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Mathematics

If A, B and C are the interior angles of a △ABC, show that : (i) cos A + B/2 = sin C/2 (ii) tan C + A/2 = cot B/2.

Trigonometrical Ratios

Related Questions

Find the value of θ (0° < θ < 90°) if :
cos 63° sec (90° - θ) = 1

Find the value of θ (0° < θ < 90°) if :
tan 35° cot (90° - θ) = 1.

Mathematics

If A, B and C are the interior angles of a △ABC, show that : (i) cos A + B/2 = sin C/2 (ii) tan C + A/2 = cot B/2.

Trigonometrical Ratios

Related Questions

Find the value of θ (0° < θ < 90°) if :cos 63° sec (90° - θ) = 1

Find the value of θ (0° < θ < 90°) if :tan 35° cot (90° - θ) = 1.

Find the value of θ (0° < θ < 90°) if :
cos 63° sec (90° - θ) = 1

Find the value of θ (0° < θ < 90°) if :
tan 35° cot (90° - θ) = 1.