(ii) দেখাও যে, \( \sin \cos ^{-1} \tan \left(\sec ^{-1} x\right)=\sqrt{2-x^{2}} \) ।

QUESTION 6 Simplify the following expressions without using a calculator. \( \begin{array}{l}6.1 \quad \frac{\sin 210^{\circ} \cos 300^{\circ} \tan 240^{\circ}}{\cos 120^{\circ} \tan 150^{\circ} \sin 330^{\circ}} \\ 6.2 \\ {[\sin (-\theta)+\cos (360-\theta)]\left[\cos (90-\theta)+\frac{\sin \theta}{\tan \theta}\right]} \\ 6.3 \text { If } \tan x=m+\frac{1}{m}, 90^{\circ} \leq x \leq 270^{\circ} \text { and } m^{2}+\frac{1}{m^{2}}=1 \\ \text { Calculate the value of } x \text { without the use of a calculator. }\end{array} \)

1) \( A=\cos ^{2} 40^{\circ}+\cos ^{2} 50^{\circ}+\tan 250 \times \cos 65^{\circ} \) 2) \( B=\cos ^{2} x \times \tan ^{2} x+\cos ^{2} s x \)

ove that \( \frac{\cos ^{2} \theta}{(\operatorname{cosec} \theta-1)(\operatorname{cosec} \theta+1)}+\frac{\sin ^{2} \theta}{(\sec \theta-1)(\sec \theta+1)}=1 \)

simplifier les exporesinions nuiveuntes: \( A=\cos ^{3} 40^{\circ}+\cos ^{2} 50^{\circ}+\tan 25^{\circ} \times \tan 65^{\circ} \) \( B=\cos ^{2} x \times \tan ^{2} x+\cos ^{2} x \)

\( \cos ^ { 2 } 40 ^ { \circ } + \cos 50 ^ { \circ } + \tan 25 ^ { \circ } \times \operatorname { san } 65 ^ { \circ } \)