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P Write the Value of Tan 10° Tan 15° Tan 75° Tan 80°? - Mathematics

Sum

Write the value of tan 10° tan 15° tan 75° tan 80°?

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Solution

We have to find: `tan10° tan 15° tan 75° tan 80°`

= `tan10° tan 15° tan 75° tan 80°`

=` tan (90°-80°) tan (90°-75°) tan 75° tan 80°`

=` cot 80° cot 75° tan 75° tan 80°`

= `(cot 75° tan 75°) (cot 80° tan 80°)` 

[tan (90°-θ)=cotθ] 

= `1xx1` `[cotθ. tan θ=1]`

=1

Hence the value of `tan10° tan 15° tan 75° tan 80°` is 1

 

 

 

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APPEARS IN

RD Sharma Class 10 Maths
Chapter 10 Trigonometric Ratios
Q 14 | Page 56
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