The value of \(\frac{\tan^2 (22^\circ - \theta)-\tan (\theta + 68^\circ)\ -\ \text{cosec}^2 (68^\circ + \theta)+\cot (22^\circ - \theta)} {3 (\cot^2 52^\circ - \sec^2 38^\circ)+ 2 (\text{cosec}^2 \ 28^\circ - \tan^2 62^\circ)}\) is:
1
The correct answer is 1.
Tangent of one angle is the cotangent of its complement. Secant of one angle is the cosecant of its complement. These identities allow us to rewrite trigonometric functions of angles greater than 45^\circ in terms of angles less than 45^\circ , which can sometimes make calculations or comparisons easier. In problems like this, recognizing complementary angles helps simplify complex expressions by converting terms into functions of the same angle.
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