Question
Download Solution PDFThe expression (tan θ + cot θ) (sec θ + tan θ) (1 – sin θ), 0° < θ < 90°, is equal to:
Answer (Detailed Solution Below)
Detailed Solution
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Given:
(tan θ + cot θ) (sec θ + tan θ) (1 – sin θ), 0° < θ < 90°
Concept Used:
Here, The exact value of θ is not given so we can put any value of theta within 0° to 90° but take that value on which none of the two options will be the same.
So, We will take θ = 30°, We will not take 45° because at 45° (1) and (2) options will be the same
Calculation:
At θ = 30° the given equation will be
(tan 30° + cot 30°) (sec 30° + tan 30°) (1 – sin 30°)
⇒
⇒
⇒ 2
Now, On putting θ = 30° in options we get
cosec 30° = 2
∴ The correct answer is cosecθ.
Alternate Method
Given:
(tan θ + cot θ) (sec θ + tan θ) (1 – sin θ), 0° < θ < 90°
Formula Used:
sin2θ + cos2θ = 1
1 - sin2θ = cos2θ
1/sinθ = cosecθ
Calculation:
⇒
⇒
⇒
⇒
⇒ cosec θ
∴ The correct answer is cosec θ.
Last updated on Jun 13, 2025
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