Question 144

What is the value of $$sec12^{0}sin12^{0}tan38^{0}tan78^{0}tan52^{0}$$?

Solution

Expression : $$sec12^{0}sin12^{0}tan38^{0}tan78^{0}tan52^{0}$$

= $$\frac{1}{cos(12^\circ)}.sin(12^\circ).tan(38^\circ).tan(78^\circ).tan(52^\circ)$$

= $$[tan(12^\circ).tan(78^\circ)].[tan(38^\circ).tan(52^\circ)]$$

Using, $$tan(90^\circ-\theta)=cot(\theta)$$

= $$[tan(12^\circ).cot(12^\circ)].[tan(38^\circ).cot(38^\circ)]$$

Also, $$tan(\theta)cot(\theta)=1$$

= $$1\times1=1$$

=> Ans - (A)

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