#### Question

Evaluate: `sin 50^@/cos 40^@ + (cosec 40^@)/sec 50^@ - 4 cos 50^@ cosec 40^@`

#### Solution

Sin 50° = sin (90° - 40°) = cos 40°

Cosec 40° = cosec (90° - 50°) = sec 50°

Cos 50° = cos (90° - 40°) = sin 40°

`=> cos 40^@/cos 40^@ + (sec 50^@)/(sec 50^@) - 4 sin 40^@ cosec 40^@`

1 + 1 – 4 = − 2 [∵ Sin 40° cosec 40° = 1]

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Evaluate Sin 50^@/Cos 40^@ + (Cosec 40^@)/Sec 50^@ - 4 Cos 50^@ Cosec 40^@ Concept: Trigonometric Ratios of Some Specific Angles.

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