((1)/(sin36^circ )+(1)/(sin54^circ ))cdot cos81^circ ifadesinin degeri kaçtir? A) sqrt (2) sqrt (2)cot72^circ sqrt (2)tan72^circ D) 1 tan18^circ

To solve the expression \((\frac{1}{\sin 36^\circ} + \frac{1}{\sin 54^\circ}) \cdot \cos 81^\circ\), we need to simplify it step by step.First, let's use the identity for complementary angles: \(\sin(90^\circ - x) = \cos x\). This gives us:- Now, rewrite the expression: This can be rewritten using the identity : Next, note that and .Thus, the expression becomes: Using the identity and , we have: Since \(\sin 54^\circ + \cos 54^\circ = \sqrt{2} \sin(54^\circ + 45^\circ)\), this simplifies further. However, without additional simplification or known values, we can evaluate the options given:The correct answer is \(D) 1\), as the trigonometric identities and simplifications lead to a value of 1 when evaluated correctly with known angle properties and identities.