From the sine and cosine formulae, we get

Dividing both numerator and denominator by formula_83, we get

Subtracting formula_85 from formula_86, using formula_87,

Similarly from the sine and cosine formulae, we get

Then by dividing both numerator and denominator by formula_90, we get

Or, using formula_92,

Using formula_94,

दोगुने कोणों की सर्वसमिकाएँ
असमिकाएँ
स्पर्शज्या (Tangent) तथा कोस्पर्शज्या (cotangent)
कैलकुलस की सर्वसमिकाएँ