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tan 7 (1 / 2) =

The given expression is \(\begin{array}{l}\tan \left(7 \frac{1^{\circ}}{2}\right) . \\ =\frac{\sin 7 \frac{1}{2}^{\circ}}{\cos 7 \frac{1}{2}^{\circ}}=\frac{\sin ^{2} 7 \frac{1}{2}^{\circ}}{\sin 7 \frac{1}{2}^{\circ} \cos... View Article

Simplify a6 – b6.

The given expression is \(\begin{array}{l}\begin{array}{l} \mathbf{a}^{6}-\mathbf{b}^{6}\\ =\left(\mathbf{a}^{2}\right)^{3}-\left(\mathbf{b}^{2}\right)^{3}\\ \left(\mathbf{a}^{3}-\mathbf{b}^{3}\right)=(\mathbf{a}-\mathbf{b})\left(\mathbf{a}^{2}+\mathbf{a b}+\mathbf{b}^{2}\right)\\ =\left(\mathbf{a}^{2}-\mathbf{b}^{2}\right)\left[\left(\mathbf{a}^{2}\right)^{2}+\mathbf{a}^{2} b^{2}+\left(\mathrm{b}^{2}\right)^{2}\right]\\ =(a+b)(a-b)\left[\left(a^{2}\right)^{2}+2 a^{2} b^{2}+\left(b^{2}\right)^{2}-a^{2} b^{2}\right]\\ =(a+b)(a-b)\left[\left(a^{2}+b^{2}\right)^{2}-a^{2} b^{2}\right]\\ =(\mathbf{a}+\mathbf{b})(\mathbf{a}-\mathbf{b})\left[\left(\mathbf{a}^{2}+\mathbf{b}^{2}+\mathbf{a b}\right)\left(\mathbf{a}^{2}+\mathbf{b}^{2}-\mathbf{a b}\right)\right]... View Article