Advertisements
Advertisements
प्रश्न
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that cos2 B + cos2 C = 1
Advertisements
उत्तर
∠A = 90°, cos B = `"AB"/"BC"`, cos C = `"AC"/"BC"`
∴ L.H.S = cos2 B + cos2 C
= `"Ab"^2/"BC"^2 + "AC"^2/"BC"^2`
= `("AB"^2 + "AC"^2)/"BC"^2`
= `"BC"^2/"BC"^2`
= 1
= R.H.S
APPEARS IN
संबंधित प्रश्न
`(5/7, (2sqrt(6))/7)` is a point on the terminal side of an angle θ in standard position. Determine the six trigonometric function values of angle θ
Find the value of the trigonometric functions for the following:
sec θ = `13/5`, θ lies in the IV quadrant
Find a quadratic equation whose roots are sin 15° and cos 15°
Prove that sin(45° + θ) – sin(45° – θ) = `sqrt(2) sin θ`
Prove that cos(A + B) cos C – cos(B + C) cos A = sin B sin(C – A)
Prove that cot(A + B) = `(cot "A" cot "B" - 1)/(cot "A" + cot "B")`
Find the value of cos 2A, A lies in the first quadrant, when cos A = `15/17`
Prove that cos 5θ = 16 cos5θ – 20 cos3θ + 5 cos θ
Prove that `32(sqrt(3)) sin pi/48 cos pi/48 cos pi/24 cos pi/12 cos pi/6` = 3
Express the following as a sum or difference
sin 4x cos 2x
Express the following as a product
cos 35° – cos 75°
Show that cot(A + 15°) – tan(A – 15°) = `(4cos2"A")/(1 + 2 sin2"A")`
If A + B + C = 180°, prove that cos A + cos B − cos C = `- 1 + 4cos "A"/2 cos "B"/2 sin "C"/2`
If A + B + C = 180°, prove that sin2A + sin2B + sin2C = 2 + 2 cos A cos B cos C
If A + B + C = 2s, then prove that sin(s – A) sin(s – B)+ sin s sin(s – C) = sin A sin B
Choose the correct alternative:
If cos 28° + sin 28° = k3, then cos 17° is equal to
Choose the correct alternative:
`(1 + cos pi/8) (1 + cos (3pi)/8) (1 + cos (5pi)/8) (1 + cos (7pi)/8)` =
Choose the correct alternative:
If `pi < 2theta < (3pi)/2`, then `sqrt(2 + sqrt(2 + 2cos4theta)` equals to
