solve this question its urgent. If you give wrong answer I'd will be reported.
Answers
Answer:
20
Step-by-step explanation:
Here's one way to do it. It's definitely not the only way. Hope it helps.
1²+2² = 5, so divide through by √5 to get
(1/√5) sin θ + (2/√5) cos θ = √3 / √5.
Let φ be such that cos φ = 1/√5 and sin φ = 2/√5. Then tan φ = 2.
Then this relation becomes
cos φ sin θ + sin φ cos θ = sin ( φ + θ ) = √3 / √5
=> cos ( φ + θ ) = ±√( 1 - 3/5 ) = ±√2 / √5
Thus
tan ( φ + θ ) = ±√3 / √2
=> ( tan φ + tan θ ) / ( 1 - tan φ tan θ ) = ±√3 / √2
=> ( 2 + tan θ ) / ( 1 - 2 tan θ ) = ±√3 / √2
=> 2 + tan θ = ±(√3/√2) ( 1 - 2 tan θ )
=> 2√2 + √2 tan θ = ±√3 - ±2√3 tan θ
=> ( √2 ± 2√3 ) tan θ = ±√3 - 2√2 ... (1)
=> ( √2 ± 2√3 ) ( -√2 ± 2√3 ) tan θ = ( ±√3 - 2√2 ) ( -√2 ± 2√3 )
=> ( 12 - 2 ) tan θ = - ±√6 + 6 + 4 - ±4√6
=> 10 tan θ = 10 - ±5√6
=> 2 tan θ = 2 - ±√6
=> 4 tan² θ = 10 - ±4√6
Also, from equation (1):
( ±√3 - 2√2 ) cot θ = √2 ± 2√3
=> ( ±√3 - 2√2 ) ( - ±√3 - 2√2 ) cot θ = ( √2 ± 2√3 ) ( - ±√3 - 2√2 )
=> ( 8 - 3 ) cot θ = - ±√6 - 4 - 6 - ±4√6
=> 5 cot θ = -10 - ±5√6
=> cot θ = - ( 2 ± √6 )
=> cot² θ = 10 ± 4√6
Finally:
4 tan² θ + cot² θ = ( 10 - ±4√6 ) + ( 10 ± 4√6 ) = 20
Answer:
20
HOPE IT HEPLS YOU......
