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In ΔABC, ∠ABC = 90° and ∠ACB = θ. Then write the ratios of sin θ and tan θ from the figure.
Concept: undefined >> undefined
Prove that sec θ + tan θ = `cos θ/(1 - sin θ)`.
Proof: L.H.S. = sec θ + tan θ
= `1/square + square/square`
= `square/square` ......`(∵ sec θ = 1/square, tan θ = square/square)`
= `((1 + sin θ) square)/(cos θ square)` ......[Multiplying `square` with the numerator and denominator]
= `(1^2 - square)/(cos θ square)`
= `square/(cos θ square)`
= `cos θ/(1 - sin θ)` = R.H.S.
∴ L.H.S. = R.H.S.
∴ sec θ + tan θ = `cos θ/(1 - sin θ)`
Concept: undefined >> undefined
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Find the value of sin 0° + cos 0° + tan 0° + sec 0°.
Concept: undefined >> undefined
Find the value of sin 45° + cos 45° + tan 45°.
Concept: undefined >> undefined
What will be the value of sin 45° + `1/sqrt(2)`?
Concept: undefined >> undefined
In the given figure, if sin θ = `7/13`, which angle will be θ?
Concept: undefined >> undefined
Prove that: cot θ + tan θ = cosec θ·sec θ
Proof: L.H.S. = cot θ + tan θ
= `square/square + square/square` ......`[∵ cot θ = square/square, tan θ = square/square]`
= `(square + square)/(square xx square)` .....`[∵ square + square = 1]`
= `1/(square xx square)`
= `1/square xx 1/square`
= cosec θ·sec θ ......`[∵ "cosec" θ = 1/square, sec θ = 1/square]`
= R.H.S.
∴ L.H.S. = R.H.S.
∴ cot θ + tan θ = cosec·sec θ
Concept: undefined >> undefined
If sec θ = `1/2`, what will be the value of cos θ?
Concept: undefined >> undefined
Find will be the value of cos 90° + sin 90°.
Concept: undefined >> undefined
In ∆RST, ∠S = 90°, ∠T = 30°, RT = 12 cm, then find RS.
Concept: undefined >> undefined
Write down the equation of a line whose slope is 3/2 and which passes through point P, where P divides the line segment AB joining A(-2, 6) and B(3, -4) in the ratio 2 : 3.
Concept: undefined >> undefined
ΔRST ~ ΔUAY, In ΔRST, RS = 6 cm, ∠S = 50°, ST = 7.5 cm. The corresponding sides of ΔRST and ΔUAY are in the ratio 5 : 4. Construct ΔUAY.
Concept: undefined >> undefined
Construct the circumcircle and incircle of an equilateral triangle ABC with side 6 cm and centre O. Find the ratio of radii of circumcircle and incircle.
Concept: undefined >> undefined
Construct the circumcircle and incircle of an equilateral ∆XYZ with side 6.5 cm and centre O. Find the ratio of the radii of incircle and circumcircle.
Concept: undefined >> undefined
Given below is the triangle and length of line segments. Identify in the given figure, ray PM is the bisector of ∠QPR.
Concept: undefined >> undefined
Given below is the triangle and length of line segments. Identify in the given figure, ray PM is the bisector of ∠QPR.
Concept: undefined >> undefined
Given below is the triangle and length of line segments. Identify in the given figure, ray PM is the bisector of ∠QPR.
Concept: undefined >> undefined
In ∆MNP, NQ is a bisector of ∠N. If MN = 5, PN = 7 MQ = 2.5 then find QP.
Concept: undefined >> undefined
Measures of some angles in the figure are given. Prove that `"AP"/"PB" = "AQ"/"QC"`.
Concept: undefined >> undefined
Find QP using given information in the figure.
Concept: undefined >> undefined
