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दिखाइए कि tan 48° tan 23° tan 42° tan 67° = 1

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Question

दिखाइए कि tan 48° tan 23° tan 42° tan 67° = 1

Sum
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Solution

tan 48° tan 23° tan 42° tan 67°

= tan (90° − 42°) tan (90° − 67°) tan 42° tan 67°

= cot 42° cot 67° tan 42° tan 67°

= (cot 42° tan 42°) (cot 67° tan 67°)

= (1) (1)

= 1

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