Question

tan theta × tan (90-theta)=​

Answer 1

Step-by-step explanation:

tan theta × cot theta ( tan 90-theta = cot theta)

Answer 2

Answer:

Correct answer is 1

tanθ⋅tan(90−θ)=tanθ×cotθ=1

∵tan(90−θ)=cotθ

STEP BY STEP

The given equation is tanθ.tan(90−θ)…………………(1)

The given equation is tanθ.tan(90−θ)…………………(1)As we know that,tan(90−θ)=cotθ …………………..(2)

The given equation is tanθ.tan(90−θ)…………………(1)As we know that,tan(90−θ)=cotθ …………………..(2)And cotθ=cosθsinθ , tanθ=sinθcosθ………………………..(3)

The given equation is tanθ.tan(90−θ)…………………(1)As we know that,tan(90−θ)=cotθ …………………..(2)And cotθ=cosθsinθ , tanθ=sinθcosθ………………………..(3)On putting the values in equation (1) which is obtained in (2) and (3) the new equation can be formulated as:

The given equation is tanθ.tan(90−θ)…………………(1)As we know that,tan(90−θ)=cotθ …………………..(2)And cotθ=cosθsinθ , tanθ=sinθcosθ………………………..(3)On putting the values in equation (1) which is obtained in (2) and (3) the new equation can be formulated as:sinθcosθ×cosθsinθ=1

The given equation is tanθ.tan(90−θ)…………………(1)As we know that,tan(90−θ)=cotθ …………………..(2)And cotθ=cosθsinθ , tanθ=sinθcosθ………………………..(3)On putting the values in equation (1) which is obtained in (2) and (3) the new equation can be formulated as:sinθcosθ×cosθsinθ=1The terms will cancel out and the value will be 1.

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