Question

Prove that cot 67=tan23

Answer 1

Answer:

cotA= tan(90-A)

so

cot 67=cot (90-23)

cot67=cot67

hence proved

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Answer 2

Step-by-step explanation:

• We know that trigonometrical relation of complementary angle

        cot (90° -α) = tan α      ...1)

• We can also write as

        67° = 90° -23°              ...2)

• To Prove that

        cot 67° = tan 23°

        Consider L.H.S

        ⇒ cot 67°

        ⇒ cot (90° -23°)         (because 67° = 90° -23°)

• From trigonometrical relation of complementary angle

        ⇒ tan 23°                    {because cot (90° -α) = tan α }

        = R.H.S    Hence proved