Question

without using trigonometry table, evaluate the following
tan35.tan40.tan45.tan50.tan55.

Answer 1

hey buddy here's your solution hope it'll help you..

given
tan35°.tan40°.tan45°.tan50°.tan55°
= tan(90°-55°).tan(90°-50°).tan45°.tan50°.tan55°
= cot55°.cot50°.tan45°.tan50°.tan55°
= cot55°.tan55°.cot50°.tan50°.tan45°
= 1×1×tan45°
= tan45°
= 1

used formula
1. tan(90°-A) = cotA
2. tanA×cotA = 1
3. and tan45° = 1

Answer 2

Here is your answer.....


tan35°.tan40°.tan45°.tan50°.tan55°

= tan(90°-55°).tan(90°-50°).tan45°.tan50°.tan55°

= cot55°.cot50°.tan45°.tan50°.tan55°

= cot55°.tan55°.cot50°.tan50°.tan45°

= 1 × 1 × tan45° [ °•° cot X . tan X = 1]

= tan 45°

= 1 [ tan 45° = 1]




...Hope it is helpful for you...