Find the value of (sec 35° / cosec 55°) - (cos 25° / sin 65°).

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Accepted Answer

Step 1: Recall the trigonometric identities and complementary angles.

Note that cosec 55° = 1/sin 55° and sec 35° = 1/cos 35°.

Step 2: Rewrite the expression:
(sec 35° / cosec 55°) - (cos 25° / sin 65°)
= (1/cos 35°) / (1/sin 55°) - (cos 25° / sin 65°)
= (1/cos 35°) * (sin 55°/1) - (cos 25° / sin 65°)
= (sin 55° / cos 35°) - (cos 25° / sin 65°)

Step 3: Use complementary angle relationships:
sin 55° = cos 35° (since sin θ = cos (90° - θ))
sin 65° = cos 25°

Step 4: Substitute these values:
= (cos 35° / cos 35°) - (cos 25° / cos 25°)
= 1 - 1
= 0

Therefore, the value of the expression is 0.

Answer

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