Advertisements
Advertisements
प्रश्न
Prove that:
(sin A + cos A) (sec A + cosec A) = 2 + sec A cosec A
Advertisements
उत्तर
(sin A + cos A) (sec A + cosec A)
= `sinA/cosA + 1 + 1 + cosA/sinA`
= `2 + (cos^2A + sin^2A)/(sinAcosA)`
= `2 + 1/(sinAcosA)`
= 2 + sec A cosec A
APPEARS IN
संबंधित प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`cos A/(1 + sin A) + (1 + sin A)/cos A = 2 sec A`
Prove the following trigonometric identities.
(1 + tan2θ) (1 − sinθ) (1 + sinθ) = 1
Prove that:
(1 + tan A . tan B)2 + (tan A – tan B)2 = sec2 A sec2 B
If 4 cos2 A – 3 = 0, show that: cos 3 A = 4 cos3 A – 3 cos A
If tan A =` 5/12` , find the value of (sin A+ cos A) sec A.
If `sin theta = x , " write the value of cot "theta .`
Four alternative answers for the following question are given. Choose the correct alternative and write its alphabet:
sin θ × cosec θ = ______
cos4 A − sin4 A is equal to ______.
Prove that sin θ (1 – tan θ) – cos θ (1 – cot θ) = cosec θ – sec θ.
If 1 + sin2α = 3 sinα cosα, then values of cot α are ______.
