If cos A = 1/2 and sin B = 1/√2, find the value of : tan A - tan B/1 + tan A tan B . Here angles A and B are from different right triangles.

Question

KnowledgeBoat · Accepted Answer

Given: cos i.e., ∴ If length of AM = 1x unit, length of AO = 2x unit. In Δ AMO, ⇒ AO2 = AM2 \+ MO2 (∵ AC is hypotenuse) ⇒ (2x)2 = (1x)2 \+ MO2 ⇒ 4x2 = 1x2 \+ MO2 ⇒ MO2 = 4x2 \- 1x2 ⇒ MO2 = 3x2 ⇒ MO = ⇒ MO = x tan And, sin i.e., ∴ If length of XY = y unit, length of YB = y unit. In Δ BXY, ⇒ YB2 = YX2 \+ BX2 (∵ AC is hypotenuse) ⇒ (y)2 = (y)2 \+ BX2 ⇒ 2y2 = y2 \+ BX2 ⇒ BX2 = 2y2 \- y2 ⇒ BX2 = y2 ⇒ BX = ⇒ BX = y tan Now, Hence, .

Mathematics

If cos A = 1/2 and sin B = 1/√2, find the value of : tan A - tan B/1 + tan A tan B . Here angles A and B are from different right triangles.

Trigonometric Identities

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