Question

tan 15° tan 25° tan 35° tan 45° tan 55° tan 65° tan 75°​

Answer 1

Step-by-step explanation:

tan15⋅tan25⋅tan45⋅tan65⋅tan75

=tan15⋅tan45⋅tan75⋅tan25⋅tan65

=tan15⋅tan(60−15)⋅tan(60+15)tan25⋅tan65

=tan(3×15)tan25tan65

=tan45⋅tan25⋅tan65

=tan25⋅tan65

=

$\frac{ \sin25.sin25 }{\ \cos25. \cos25 }$

cos(25+65)+cos(25−65)

cos(25−65)−cos(25+65)

=

0+cos40

cos40−0

=1

Answer 2

Your answer is 1

solution;

=>tan15°× tan25°× tan35°×1 (as tan 45°=1)

×tan (90°-35°) × tan (90°-25°) × tan (90°-15°)

now, we know, tan (90°-$)=cot $

=>tan15°× tan25°× tan 35°× cot35°× cot25°× cot15°

we know that tan $× cot $=1

=>(tan15°× cot15°)× (tan25°× cot25°)× (tan35°× cot35°)

=>1×1×1

=>1

hence your answer is 1.